Backtracking

Safety critical software requires integrating verification techniques in software development methods. Software architectures must guarantee that developed systems will meet safety requirements and safety analyses are frequently used in the assessment. Safety engineers and software architects must reach a common understanding on an optimal architecture from both perspectives. Currently both groups of engineers apply different modelling techniques and languages: safety analysis models and software modelling languages. The solutions proposed seek to integrate both domains coupling the languages of each domain. It constitutes a sound example of the use of language engineering to improve efficiency in a software-related domain. A model-driven development approach and the use of a platform-independent language are used to bridge the gap between safety analyses (failure mode effects and criticality analysis and fault tree analysis) and software development languages (e.g. unified modelling language). Language abstract syntaxes (metamodels), profiles, language mappings (model transformations) and language refinements, support the direct application of safety analysis to software architectures for the verification of safety requirements. Model consistency and the possibility of automation are found among the benefits.

Abstract: In this paper we present a backtracking version of the survey propagation algorithm. We show that the introduction of the simplest form of backtracking greatly improves the ability of the original survey propagation algorithm in solving difficult random problems near the sat-unsat transition.

Sudoku is a pretty popular number game. The goal of this game is to fill a 9x9 matrix with unique numbers, and there should not be repeated numbers in each row, column, or block. This paper proposed a solution to solve Sudoku using the Backtracking Algorithm. This algorithm is quite efficient because it does not have to check all the possibilities that exist, but which leads to only the solution that will be processed, namely by pruning every element that does not lead to the solution. Thus the time required is quite efficient and suitable for use in reasonably complex numbers games like sudoku. By implementing the backtracking algorithm in the sudoku game, the complexity of the algorithm can be as large 𝜽 (n3).

Undeva, prin preajma anului '94, un elev de clasa a XI-a se gândea să-şi construiască un unit Pascal care să îl ajute la implementarea rapidă a metodei backtracking. Pentru aceasta avea la îndemână un singur atu, care era repetat la nesfârşit în toate cărţile de informatică, ce tratau această metodă: backtracking-ul se aplică problemelor a căror soluţie se poate reprezenta sub forma unui vector... Deci, la prima vedere nimic dificil. Totul consta în a specifica care sunt elementele acelui vector, care sunt condiţiile de continuare şi  care sunt condiţiile finale..., iar apoi soluţia ieşea ca pe bandă. Dar, abia mai târziu, acel elev (care de fapt eram eu) a înţeles că de fapt dificultatea unei probleme de informatică nu constă în determinarea tipului de algoritm care se aplică, ci în rezolvarea sutelor şi miilor de cazuri mărunţele care apar în jurul acesteia, cu alte cuvinte, de la soluţie care se poate reprezenta sub forma unui vector până efectiv la soluţie este o cale lungă şi spinoasă.
Puţin mai târziu, după ce am studiat bine şi celelalte metode de programare am dedus că fiecare dintre ele are un algoritm general de rezolvare, dar care nu era aşa de evident precum cel de la backtracking tocmai din cauză că la această metodă se sugera structura de date care trebuie folosită, şi anume un vector. Acum, când scriu aceste rânduri nu mi se mai pare aşa de dificilă găsirea unui algoritm general pentru o clasă de probleme. Pur şi simplu se foloseşte metoda rafinării în paşi succesivi. Adică, ca să fiu puţin mai explicit, se pleacă de la o problemă pentru care se scrie un algoritm. Apoi se analizează o altă problemă din aceeaşi clasă şi algoritmul iniţial se rescrie astfel încât să poată rezolva ambele probleme. Apoi se mai analizează încă o problemă... Şi nu trebuie să se continue această operaţie de mai mult de 10 (zece) ori, adică, cu alte cuvinte dacă se reuşeşte analizarea şi combinarea a 10 algoritmi reprezentativi, atunci rezultatul este suficient de general pentru a rezolva multe probleme din aceea clasă.

Programul nu l-am conceput ca pe un creator de elemente soft orientate pe metodele de programare. El este un mijloc şi nu un scop. De fapt este un mijloc pentru a crea un alt mijloc pe care îl voi folosi la crearea unui alt mijloc... etc, dar niciodată nu voi ajunge să creez un scop. Toată viaţa nu vom face altceva decât să creăm mijloace, adică lucruri care ne vor ajuta să creăm alte lucruri.

Despite the power of Parser Expression Grammars (PEGs) and GLR, parsing is not a solved problem. Adding nondeterminism (parser speculation) to traditional LL and LR parsers can lead to unexpected parse-time behavior and introduces practical issues with error handling, single-step debugging, and side-effecting embedded grammar actions. This paper introduces the LL(*) parsing strategy and an associated grammar analysis algorithm that constructs LL(*) parsing decisions from ANTLR grammars. At parse-time, decisions gracefully throttle up from conventional fixed k ≥ 1 lookahead to arbitrary lookahead and, finally, fail over to backtracking depending on the complexity of the parsing decision and the input symbols. LL(*) parsing strength reaches into the context-sensitive languages, in some cases beyond what GLR and PEGs can express. By statically removing as much speculation as possible, LL(*) provides the expressivity of PEGs while retaining LL's good error handling and unrestricted grammar actions. Widespread use of ANTLR (over 70,000 downloads/year) shows that it is effective for a wide variety of applications.

The value of depth-first search or "bacltracking" as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components of a directed graph and ar algorithm for finding the biconnected components of an undirect graph are presented. The space and time requirements of both algorithms are bounded by k 1V + k2E d-k for some constants kl, k2, and k a, where Vis the number of vertices and E is the number of edges of the graph being examined.

Sungka is an indigenous Philippine board game played by two players in which winning can be through a series of moves that result in capturing all the opponent's counters in the second round without giving the latter the chance to move. Being a zero-sum, finite, and deterministic game of perfect information, sungka and its close counterparts in other areas of the world have offered scholars in the computing field some solution spaces, which may not be possibly attainable using only human problem-solving skills. This paper finds winning second round openings for different board configurations, describes the nature of human-found solutions, and presents the machinefound solutions including the processor speedup that the latter attained.

Backtrack programming is such a powerful technique for problem solving that a number of languages, especially in the area of artificial intelligence, have built-in facilities for backtrack programming. This paper describes CBack, a simple, but general tool for backtrack programming in the programming language C. The use of the tool is illustrated through examples of a tutorial nature. In addition to the usual depth-first search strategy, CBack provides for the more general heuristic best-first search strategy. The implementation of CBack is described in detail. The source code, shown in its full length, is entirely written in ANSI C and highly portable across diverse computer architectures and C compilers.

Algoritma dapat digunakan untuk menyelesaikan berbagai macam permasalahan, salah satunya dapat digunakan dalam penyelesaian permainan teka-teki silang. Dalam permainan teka-teki silang pemain diharuskan mengisi kotak mendatar dan menurun dengan kata yang sudah disediakan. Permainan Tekateki silang ini termasuk CSP(Constraint Satisfaction Problem)[2] atau pendekatan yang bersifat matematis untuk menemukan jawaban dengan memenuhi jumlah persyaratan (jumlah kotak). Pada tulisan ini akan dibahas penyelesaian teka-teki silang menggunakan algoritma backtracing/runut-balik Dengan menggunakan algoritma backtracking  diharapkan penyelesaian permainan teka-teki silang dapat lebih mudah diselesaikan. Dengan metode ini proses penyelesaian yang dilakukan adalah menyesuaikan kotak dengan jumlah huruf lalu penyesuain dengan huruf yang bersilang antara kotak mendatar dan menurun. Jika tidak ditemukan kesesuaian maka dilakukan backtracking.

On the standard analysis, a counterfactual conditional such as “If P had been the case, then Q would have been the case” is true in the actual world if, in all nearest possible worlds in which its antecedent (P) is true, its consequent (Q) is also true. Despite its elegance, this analysis faces a difficulty if the laws of nature are deterministic. Then the antecedent could not have been true, given prior conditions. So, it is unclear what the relevant “nearest possible worlds” are. David Lewis suggested that they are ones in which a local breach of the laws occurred: a “small miracle”. Others have suggested that they are ones in which the initial conditions were different (“backtracking”). I propose another response. It builds on the idea that the special sciences, where counterfactual reasoning is most common, operate at a higher level of description from fundamental physics, and that the world may behave indeterministically at higher levels even if it behaves deterministically at the fundamental physical one. The challenge from determinism can then be bypassed for many special-science counterfactuals.

We present a tool for the automated generation of unit tests. It symbolically executes Java bytecode in order to find execution paths through a program. To efficiently accomplish this task, it uses constraint solving, choice-point generation and backtracking. As the number of test cases found might be very high and most of them are redundant, we propose a novel way to eliminate test cases based on their contribution to the global coverage of the controlflow and data-flow. Besides discussing the techniques used to achieve this, we present experimental results to prove the feasibility of our approach.

In this paper, we present a general algorithm which gives an uniform view of several state-of-the-art systematic backtracking search algorithms for solving both binary and nonbinary CSP instances. More precisely, this algorithm integrates the most usual or/and sophisticated look-back and look-ahead schemes. By means of this algorithm, our purpose is then to study the interest of backjump-based techniques with respect to conflict-directed variable ordering heuristics.

We propose a model called priority branching trees (pBT ) for backtracking and dynamic programming algorithms. Our model generalizes both the priority model of Borodin, Nielson and Rackoff, as well as a simple dynamic programming model due to Woeginger, and hence spans a wide spectrum of algorithms. After witnessing the strength of the model, we then show its limitations by providing lower bounds for algorithms in this model for several classical problems such as Interval Scheduling, Knapsack and Satisfiability.

Materials that must be transported upstream in a production line along a linear track are said to backtrack. In this line, management attempts to simplify the workflow of jobs by assigning machines to appropriate locations along the line to minimize backtracking. The problem of assigning M machines to M locations along a linear track to minimize the total backtracking of jobs forms a quadratic assignment problem (QAP) and is a difficult task; an optimum solution to such a problem with large M is computationally intractable. Therefore, an efficient, depth-first insertion heuristic is used here to improve the solution obtained by a construction heuristic, called multi-pass heuristic. A lower bound to assess the quality, and a measure of backtracking to assess the proximity of a configuration to a generalized flow line are developed in this paper. In addition to computational results, a simulation model is also used to assess the effect of reducing backtracking on overall system performance in a dynamic environment.

We address the problem of scheduling applications represented as directed acyclic task graphs (DAGs) onto architectures with reconfigurable processing cores. We introduce the Mutually Exclusive Processor Groups reconfiguration model, a novel reconfiguration model that captures many different modes of reconfiguration. Additionally, we propose the Heterogeneous Earliest Finish Time with Mutually Exclusive Processor Groups (HEFT-MEG) scheduling heuristic using the Mutually Exclusive Processor Groups reconfiguration model. HEFT-MEG schedules reconfigurations using a novel back-tracking algorithm to evaluate how different reconfiguration decisions affect previously scheduled tasks. HEFT-MEG's goal when choosing configurations is to choose the most efficient configuration for different application phases. In simulation, HEFT-MEG generates higher quality schedules than those generated by the hardware-software co-scheduler proposed by Mei, et al. [16] and HEFT [26] using a single configuration.

To achieve high Strapdown Inertial Navigation System (SINS) alignment accuracy within a short period of time is still a challenging issue for underwater vehicles. In this paper, a new SINS initial alignment scheme aided by the velocity derived from Doppler Velocity Log (DVL) is proposed to solve this problem. In the stage of the coarse alignment, the velocity of DVL is employed to reduce the impact of the linear motion. With a backtracking framework, the fine alignment runs with the data recorded during the process of the coarse alignment and thus will speed up the overall alignment process. In addition, by using this new scheme, it is equivalent to length the alignment time for both coarse and fine alignments, so the accuracy of the alignments will be improved. In order to reduce the volume of the data that has to be recorded, a new model for SINS fine alignment is derived in the inertial reference frame which makes it feasible for real time applications. The experimental results are presented for both unaided static and in-motion alignment using DVL aiding. It is clearly shown that the proposed method meets the requirement of SINS alignment for underwater vehicles.

Safety critical software requires integrating verification techniques in software development methods. Software architectures must guarantee that developed systems will meet safety requirements and safety analyses are frequently used in the assessment. Safety engineers and software architects must reach a common understanding on an optimal architecture from both perspectives. Currently both groups of engineers apply different modelling techniques and languages: safety analysis models and software modelling languages. The solutions proposed seek to integrate both domains coupling the languages of each domain. It constitutes a sound example of the use of language engineering to improve efficiency in a software-related domain. A model-driven development approach and the use of a platform-independent language are used to bridge the gap between safety analyses (failure mode effects and criticality analysis and fault tree analysis) and software development languages (e.g. unified modelling language). Language abstract syntaxes (metamodels), profiles, language mappings (model transformations) and language refinements, support the direct application of safety analysis to software architectures for the verification of safety requirements. Model consistency and the possibility of automation are found among the benefits.

Algoritma Backtracking (Runut-Balik) merupakan algoritma yang sangat baik dalam
menyelesaikan permasalahan yang memiliki banyak kemungkinan karena algoritma
ini tidak memeriksa semua kemungkinan yang ada. Algoritma ini hanya
mempertimbangkan kemungkinan yang mengarah kepada solusi, sehingga proses
pencarian menjadi jauh lebih cepat. Algoritma Multiplicative CRNG adalah
algoritma pembangkit bilangan acak yang baik karena tidak membangkitkan
bilangan yang sama secara berturut-turut. Pembangkit dan penyelesai permainan
Sudoku Hijaiyah merupakan permasalahan yang dapat diselesaikan dengan baik
menggunakan perpaduan antara algoritma Backtracking dan algoritma
Multiplicative CRNG.

In this article presents applications of Backtracking method using object -oriented programming in C #. Object-oriented programming means programs with new types that integrates both data and methods associated with the creation, processing and destruction of such data. To gain advantages through abstraction programming (the program is no longer a succession of processing, but a set of objects to life (Figure 1), have different properties, are capable of specific actions and interact in the program). Spoke on instantiation new techniques, derivation and polimorfismul object types.

Mobile robots need to explore novel environments to build useful maps for later navigation and motion planning. Sensor-based Random Tree, (SRT), technique had been used for exploration but it is problematic since the robot may visit the same place more than one time during backtracking process. In this paper, we propose a new heuristic algorithm to reduce this backtracking problem using the obtained map data. This algorithm is tested through computer simulations for several scenarios. The performance is evaluated in terms of exploration time, travelled distance and number of visited nodes. Since these classical evaluation metrics are correlated, we propose a new evaluation metric, that combines the total performance. The new algorithm is confirmed to reduce the exploration time of up to 30 %. The new evaluation metric is also shown to encapsulate the exploration performance and can be regarded as a much better representative of the performance that facilitate comparisons.

Stochastic Boolean satisfiability (SSAT) is a generalization of satisfiability (SAT) that has shown promise as a vehicle for encoding and competitively solving probabilistic reasoning problems. We extend the theory and enhance the applicability of SSAT-based solution techniques by 1) establishing theoretical results that allow the incorporation of nonchronological backtracking (NCB), and lay the foundation for the incorporation of learning, into an SSAT solver, 2) implementing SOLVESSAT-NCB, an NCBaugmented SSAT solver, and 3) describing the results of tests of SOLVESSAT-NCB on randomly generated SSAT problems and SSAT encodings of probabilistic planning problems. Our experiments indicate that NCB has the potential to boost the performance of an SSAT solver, both in terms of time, yielding speedups of as much as five orders of magnitude, and space, allowing the solution of SSAT problems with larger solution trees. In some cases, however, NCB can degrade performance. We analyze the reasons for this behavior, present initial results incorporating a technique to mitigate this effect, and discuss other approaches to addressing this problem suggested by our empirical results.

Secure your wireless networks against attacks, hacks, and intruders with this step-by-step guide Overview Make your wireless networks bulletproof Easily secure your network from intruders See how the hackers do it and learn how to defend yourself In Detail Wireless networks are everywhere. You have probably set one up yourself, but have you ever wondered just how safe you are while browsing online? In the majority of cases, the default settings for your networks are not enough to protect you. With your data being transferred over the air, it can be easily plucked and used by anyone who knows how. Don't let it happen to you. BackTrack - Testing Wireless Network Security will help you secure your wireless networks and keep your personal data safe. With this book, you will learn how to configure your hardware for optimum security, find network security holes, and fix them. BackTrack - Testing Wireless Network Security looks at what tools hackers use and shows you how to defend your...

Most CSP algorithms are based on refinements and extensions of backtracking, and employ one of two simple "branching schemes": 2-way branching or d-way branching, for domain size d. The schemes are not equivalent, but little is known about their relative power. Here we compare them in terms of how efficiently they can refute an unsatisfiable instance with optimal branching choices, by studying two variants of the resolution proof system, denoted C-RES and NG-RES , which model the reasoning of CSP algorithms. The tree-like restrictions, tree-C-RES and tree-NG-RES , exactly capture the power of backtracking with 2-way branching and d-way branching, respectively. We give a family instances which require exponential sized search trees for backtracking with d-way branching, but have size O(d 2 n) search trees for backtracking with 2way branching. We also give a natural branching strategy with which backtracking with 2-way branching finds refutations of these instances in time O(d 2 n 2). The unrestricted variants of C-RES and NG-RES can simulate the reasoning of algorithms which incorporate learning and k-consistency enforcement. We show exponential separations between C-RES and NG-RES , as well as between the tree-like and unrestricted versions of each system. All separations given are nearly optimal.

The average time required by backtracking is analyzed over four models of random conjunctive normal form formulas. Each model gives a result of exp(0(I'(' n)/(r-")), where o is the number of variables from which literals may be formed. s is the number of literals per clause, and o" (1 < a < s) is the number of clauses in the predicate. This indicates that the analysis methods used are insensitive to small changes in the random model.

Beam search (BS) is used as a heuristic to solve various combinatorial optimization problems, ranging from scheduling to assembly line balancing. In this paper, we develop a backtracking and an exchange-of-information (EOI) procedure to enhance the traditional beam search method. The backtracking enables us to return to previous solution states in the search process with the expectation of obtaining better solutions. The EOI is used to transfer information accumulated in a beam to other beams to yield improved solutions. We developed six different versions of enhanced beam algorithms to solve the mixed-model assembly line scheduling problem. The results of computational experiments indicate that the backtracking and EOI procedures that utilize problem specific information generally improve the solution quality of BS.

A heuristic algorithm for solving the single-hoist, multiple-product scheduling problem is presented. The algorithm uses a non-standard Constraint Satisfaction Problem (CSP) model and employs variable ordering, forward checking and backtracking. Computational results, including comparison with existing algorithms in terms of solution quality and speed, are presented.

Integrated development environments (IDEs) increase programmer productivity, providing rapid, interactive feedback based on the syntax and semantics of a language. A heavy burden lies on developers of new languages to provide adequate IDE support. Code generation techniques provide a viable, efficient approach to semi-automatically produce IDE plugins. Key components for the realization of plugins are the language's grammar and parser. For embedded languages and language extensions, constituent IDE plugin modules and their grammars can be combined. Unlike conventional parsing algorithms, scannerless generalized-LR parsing supports the full set of context-free grammars, which is closed under composition, and hence can parse language embeddings and extensions composed from separate grammar modules. To apply this algorithm in an interactive environment, this paper introduces a novel error recovery mechanism, which allows it to be used with files with syntax errors -common in interactive editing. Error recovery is vital for providing rapid feedback in case of syntax errors, as most IDE services depend on the parser -from syntax highlighting to semantic analysis and cross-referencing. We base our approach on the principles of island grammars, and derive permissive grammars with error recovery productions from normal SDF grammars. To cope with the added complexity of these grammars, we adapt the parser to support backtracking. We evaluate the recovery quality and performance of our approach using a set of composed languages, based on Java and Stratego.

When a large oil or gas field is produced, several reservoirs often share the same processing facility. This facility is typically capable of processing only a limited amount of commodities per unit of time. In order to satisfy these processing limitations, the production needs to be choked, i.e., scaled down by a suitable choke factor. A production strategy is defined as a vector valued function defined for all points of time representing the choke factors applied to reservoirs at any given time. In the present paper we consider the problem of optimizing such production strategies with respect to various types of objective functions. A general framework for handling this problem is developed. A crucial assumption in our approach is that the potential production rate from a reservoir can be expressed as a function of the remaining recoverable volume. The solution to the optimization problem depends on certain key properties, e.g., convexity or concavity, of the objective function and of the potential production rate functions. Using these properties several important special cases can be solved. An admissible production strategy is a strategy where the total processing capacity is fully utilized throughout a plateau phase. This phase lasts until the total potential production rate falls below the processing capacity, and after this all the reservoirs are produced without any choking. Under mild restrictions on the objective function the performance of an admissible strategy is uniquely characterized by the state of the reservoirs at the end of the plateau phase. Thus, finding an optimal admissible production strategy, is essentially equivalent to finding the optimal state at the end of the plateau phase. Given the optimal state a backtracking algorithm can then used to derive an optimal production strategy. We will illustrate this on a specific example.

Subgraph isomorphism is a fundamental graph problem with many important applications. Given two graphs G and SG, the subgraph isomorphism problem is to determine whether G contains a subgraph that is isomorphic to SG. It is well known that the problem is NP complete in the worst case. In this paper, we present two new algorithms for subgraph isomorphism problem for labeled graphs. If the graphs have unique vertex labels, we designed a new algorithm based on modified adjacency list that has achieved linear performance. For general graphs we present another algorithm using optimized backtracking search. Though this algorithm doesn't guarantee polynomial time, it reduces the search space by applying several pruning techniques. Simulation results show that our new algorithms are competitive with classic Ullman's algorithm and more recent VF2.

It is known that Particle Filter and Map Filtering techniques can be used to improve the performance of positioning systems, such as Pedestrian Dead Reckoning (PDR). In previous research on indoor navigation, it was generally assumed that detailed building plans were available. However, in many emergency / rescue scenarios, there may be only limited building plan information on hand. The purpose of this paper is to show how a novel Backtracking Particle Filter (BPF) can be combined with different levels of building plan detail to improve PDR performance.

The mathematical theory of reliability has grown out of the demand of modern technology and particularly out of the experience with complex systems. The main objective is to enhance the ability of such complex network systems. This work present an efficient algorithm, which is a novel approach to generate all the minimal paths of the general flow network based on the principle of backtracking. It is a general flow network because, the proposed approach can find the minimal paths for multiple sources and multiple sinks in the network. One can further evaluate the network reliability using any existing SDP (Sum of Disjoint Products) based approach.

Algoritma Backtracking (Runut-Balik) merupakan algoritma yang sangat baik dalam menyelesaikan permasalahan yang memiliki banyak kemungkinan karena algoritma ini tidak memeriksa semua kemungkinan yang ada. Algoritma ini hanya mempertimbangkan kemungkinan yang mengarah kepada solusi, sehingga proses pencarian menjadi jauh lebih cepat. Algoritma Multiplicative CRNG adalah algoritma pembangkit bilangan acak yang baik karena tidak membangkitkan bilangan yang sama secara berturut-turut. Pembangkit dan penyelesai permainan Sudoku Hijaiyah merupakan permasalahan yang dapat diselesaikan dengan baik menggunakan perpaduan antara algoritma Backtracking dan algoritma Multiplicative CRNG.

AbstractÐThis paper introduces GRASP (Generic seaRch Algorithm for the Satisfiability Problem), a new search algorithm for Propositional Satisfiability (SAT). GRASP incorporates several search-pruning techniques that proved to be quite powerful on a wide variety of SAT problems. Some of these techniques are specific to SAT, whereas others are similar in spirit to approaches in other fields of Artificial Intelligence. GRASP is premised on the inevitability of conflicts during the search and its most distinguishing feature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack nonchronologically to earlier levels in the search tree, potentially pruning large portions of the search space. In addition, by ªrecordingº the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Finally, straightforward bookkeeping of the causality chains leading up to conflicts allows GRASP to identify assignments that are necessary for a solution to be found. Experimental results obtained from a large number of benchmarks indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely effective for a large number of representative classes of SAT instances.

The multi-paradigm language PROGRES is the first rule-ori- ented visual language which has a well-defined type concept and supports programming with graph rewriting systems. To some extent, it has the flavor of a visual database program- ming language with powerful pattern matching and replac- ing facilities as well as backtracking capabilities. Until now, it was mainly used for specifying and

Breaking a big integer into two factors is a famous problem in the field of Mathematics and Cryptography for years. Many crypto-systems use such a big number as their key or part of a key with the assumption - it is too big that the fastest factorisation algorithms running on the fastest computers would take impractically long period of time to factorise. Hence, many efforts have been provided to break those crypto-systems by finding two factors of an integer for decades. In this paper, a new factorisation technique is proposed which is based on the concept of backtracking. Binary bit by bit operations are performed to find two factors of a given integer. This proposed solution can be applied in computing square root, primality test, finding prime factors of integer numbers etc. If the proposed solution is proven to be efficient enough, it may break the security of many crypto-systems. Implementation and performance comparison of the technique is kept for future research.

We study here the problem of solving the traditional n-queens puzzle by a group of homogeneous reactive robots. We have devised two general and decentralized behaviour-based algorithms that solve the puzzle for N mobile robots. They all make a depth-first search with backtracking "in the wild" guaranteeing "in principle" a solution. In the first one, there is a predefined precedence order in the group; each robot has local sensing (sonar), a GPS, and is able to communicate with the previous and next group elements. In the other algorithm, there is only local sensing ability and a GPS. There is neither a predefined group order nor any peer-to-peer communication between the robots. We have validated our algorithms in a simulation context.

Stochastic Boolean satisfiability (SSAT) is a generalization of satisfiability (SAT) that has shown promise as a vehicle for encoding and competitively solving probabilistic reasoning problems. We extend the theory and enhance the applicability of SSAT-based solution techniques by 1) establishing theoretical results that allow the incorporation of nonchronological backtracking (NCB), and lay the foundation for the incorporation of learning, into an SSAT solver, 2) implementing SOLVESSAT-NCB, an NCBaugmented SSAT solver, and 3) describing the results of tests of SOLVESSAT-NCB on randomly generated SSAT problems and SSAT encodings of probabilistic planning problems. Our experiments indicate that NCB has the potential to boost the performance of an SSAT solver, both in terms of time, yielding speedups of as much as five orders of magnitude, and space, allowing the solution of SSAT problems with larger solution trees. In some cases, however, NCB can degrade performance. We analyze the r...

A new approach to extract knowledge from multispectral images is suggested. We describe a method to extract and optimize classification rules using fuzzy neural networks (FNNs). The FNNs consist of two stages. The first stage represents a fuzzifier block, and the second stage represents the inference engine. After training, classification rules are extracted by backtracking along the weighted paths through the FNN. The extracted rules are then optimized by use of a fuzzy associate memory bank. We use the algorithm to extract classification rules from a multispectral image obtained with a Landsat Thematic Mapper sensor. The scene represents the Mississippi River bottomland area. In order to verify the rule extraction method, measures such as the overall accuracy, producer's accuracy, user's accuracy, kappa coefficient, and fidelity are used.