In this chapter we will give an outline of applications of logic functions and equations that are... more In this chapter we will give an outline of applications of logic functions and equations that are not directly related to the design of hardware. The applications in propositional logic are surely the oldest and reach back to the developments of science in ancient Greece. The names Boolean Algebra and Boolean Ring have been selected in honor of George Boole who wanted to formalize the ideas expressed by texts in natural language and to calculate the truth of complex constructions (in order to be precise and more accurate). Naturally we already had to use logic in this sense throughout the book, however, we will go back to an introductory or elementary point of view and show that the knowledge that has been prepared up to now is fully appropriate to solve these problems. There was an enormous development of logic (in a broad mathematical sense) during the last 150 years that resulted in a highly sophisticated and specialized level, however, the propositional calculus is still the foundation of all these developments, and it is still necessary and useful to have a good understanding of these concepts. Binary arithmetic is widely used in computer hardware, control systems, or other electronic devices. In this chapter we will give an outline of binary Mathematics before hardware-related problems will be discussed in more detail. Coding is a unique mapping of arbitrary objects to certain code words. Binary codes can be seen as bridges between many real world areas and logic functions. The code words can be a subset of a given finite set so that changes of one or more bits can be detected or even corrected. The introduced Specific Normal Form uniquely expresses a logic function, differs significantly from other known normal forms, and has several remarkable properties. This new normal form is used to find the most complex logic functions and to classify bent functions. Bent functions are logic functions having the largest distance to all linear function which is a useful property for cryptographic applications.
Abstract. The calculation of Hamiltonian Circuits is an NP-complete task. This paper uses slightl... more Abstract. The calculation of Hamiltonian Circuits is an NP-complete task. This paper uses slightly modified complete sets of Hamiltonian circuits for the classification of documents. The solution method is based on a SAT-instance with a huge number of clauses which is flattening the knowledge about the problem. We suggest an even more compact model of Boolean equations that preserves the knowledge by summarizing restrictions and requirements. The presented implicit two-phase SAT-solver finds efficiently the solution using operations of the XBOOLE library. This solver can be included easily as signal processing unit into the device where the classification of the documents is required. 1
This paper presented a FPGA design of SEED, which is the Korea standard 128-bit block cipher. In ... more This paper presented a FPGA design of SEED, which is the Korea standard 128-bit block cipher. In this work, SEED was designed technology-independently for other applications such as ASIC or core-based designs. Hence in case of changing the target of design, it is not necessary to modify design or need only minor modification to reuse the design. Since SEED algorithm requires a lot of hardware resources, each unit was designed only once and used sequentially. So, the number of gates was minimized and SEED algorithm was fitted in FPGA without additional components. It was confirmed that the rate of resource usage is about 80% in ALTERA 10KE and the SEED design operates in a clock frequency of 131.57 MHz and an encryption rate of 29 Mbps.
In this paper we use Boolean models to generate new results in Combinatorics. On the one hand, th... more In this paper we use Boolean models to generate new results in Combinatorics. On the one hand, these new results answer real questions which have not been solved so far. On the other hand, these new results can immediately be useful for future applications. We emphasize a new sequence of numbers which we call, due to the analyzed problem, the sequence of Bishop numbers. It will also be very useful to study the methodology that has been applied. Any problem that can be converted into a Boolean model can be solved for a broad range of parameters in a constructive way. It is not only known that there are solutions, the results will be fully available. This relates particularly to all constraint-related problems, even when the Boolean models are very complex.
Proceedings of 1995 IEEE International Conference on Fuzzy Systems. The International Joint Conference of the Fourth IEEE International Conference on Fuzzy Systems and The Second International Fuzzy Engineering Symposium
The application of knowledge which can be considered only incompletely and imprecisely and the co... more The application of knowledge which can be considered only incompletely and imprecisely and the combination of this knowledge by means of evaluation functions results in uncertain values. In many search algorithms, this uncertainty simply is ignored by using only the resulting (crisp) value. It is assumed that the consideration of this uncertainty in search algorithms will give better results. The
Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94)
Page 1. Neural Network Learning in a Chess Endgame Christian Posthoff, Stanislaw Schawelski, Mich... more Page 1. Neural Network Learning in a Chess Endgame Christian Posthoff, Stanislaw Schawelski, Michael Schlosser Dept. ... These two chessmen are alone active during the play. For more details see [SCHLOSSER 921. Main results of this EDB construction (cf. [SCHLOSSER ...
Proceedings Intelligent Information Systems. IIS'97
The learning of propositional and fuzzy-logical functions and structures has been thoroughly expl... more The learning of propositional and fuzzy-logical functions and structures has been thoroughly explored in the past years and has become an efficient means for knowledge acquisition. Decision trees are broadly discussed and used, many algorithms for the learning of optimal decision trees are available. Publications and implementations, however, very often show a considerable lack of understanding of the capacities and
Algorithms for Games aims to provide a concrete example of the programming of a two-person game w... more Algorithms for Games aims to provide a concrete example of the programming of a two-person game with complete information, and to demonstrate some of the methods of solutions; to show the reader that it is profitable not to fear a search, but rather to undertake it in a rational fashion, make a proper estimate of the dimensions of the "catastrophe", and use all suitable means to keep it down to a reasonable size. The book is dedicated to the study of methods for limiting the extent of a search. The game programming problem is very well suited to the study of the search problem, and in general for multi-step solution processes. With this in mind, the book focuses on the programming of games as the best means of developing the ideas and methods presented. While many of the examples are related to chess, only an elementary knowledge of the game is needed.
This position statement provides guidelines for assessing risk associated with carotid endarterec... more This position statement provides guidelines for assessing risk associated with carotid endarterectomy and defines the point at which risk is too high to perform surgery for specific indications described below. Morbidity and mortality levels are discussed. This statement does not address indications for surgery or merits of specific medical or surgical treatments. Results of current studies that compare relative risk of various treatments for carotid artery disease are not yet available.
Abstract—This paper aims at the classiffication of bent functions in order to allow their constru... more Abstract—This paper aims at the classiffication of bent functions in order to allow their construction without searching or sieving. We focus on the characterization of bent functions in the context of Specialized Normal Forms. Furthermore we want to express bent functions in terms of derivative operations of the Boolean Differential Calculus. In order to solve these problems, we study bent functions of two and four variables in detail. This exploration leads finally to Boolean differential equations that will allow the direct calculation of bent functions. Keywords-bent function; classification; specialized normal form; Boolean Differential Calculus; Boolean differential equation; XBOOLE.
In this chapter we will give an outline of applications of logic functions and equations that are... more In this chapter we will give an outline of applications of logic functions and equations that are not directly related to the design of hardware. The applications in propositional logic are surely the oldest and reach back to the developments of science in ancient Greece. The names Boolean Algebra and Boolean Ring have been selected in honor of George Boole who wanted to formalize the ideas expressed by texts in natural language and to calculate the truth of complex constructions (in order to be precise and more accurate). Naturally we already had to use logic in this sense throughout the book, however, we will go back to an introductory or elementary point of view and show that the knowledge that has been prepared up to now is fully appropriate to solve these problems. There was an enormous development of logic (in a broad mathematical sense) during the last 150 years that resulted in a highly sophisticated and specialized level, however, the propositional calculus is still the foundation of all these developments, and it is still necessary and useful to have a good understanding of these concepts. Binary arithmetic is widely used in computer hardware, control systems, or other electronic devices. In this chapter we will give an outline of binary Mathematics before hardware-related problems will be discussed in more detail. Coding is a unique mapping of arbitrary objects to certain code words. Binary codes can be seen as bridges between many real world areas and logic functions. The code words can be a subset of a given finite set so that changes of one or more bits can be detected or even corrected. The introduced Specific Normal Form uniquely expresses a logic function, differs significantly from other known normal forms, and has several remarkable properties. This new normal form is used to find the most complex logic functions and to classify bent functions. Bent functions are logic functions having the largest distance to all linear function which is a useful property for cryptographic applications.
Abstract. The calculation of Hamiltonian Circuits is an NP-complete task. This paper uses slightl... more Abstract. The calculation of Hamiltonian Circuits is an NP-complete task. This paper uses slightly modified complete sets of Hamiltonian circuits for the classification of documents. The solution method is based on a SAT-instance with a huge number of clauses which is flattening the knowledge about the problem. We suggest an even more compact model of Boolean equations that preserves the knowledge by summarizing restrictions and requirements. The presented implicit two-phase SAT-solver finds efficiently the solution using operations of the XBOOLE library. This solver can be included easily as signal processing unit into the device where the classification of the documents is required. 1
This paper presented a FPGA design of SEED, which is the Korea standard 128-bit block cipher. In ... more This paper presented a FPGA design of SEED, which is the Korea standard 128-bit block cipher. In this work, SEED was designed technology-independently for other applications such as ASIC or core-based designs. Hence in case of changing the target of design, it is not necessary to modify design or need only minor modification to reuse the design. Since SEED algorithm requires a lot of hardware resources, each unit was designed only once and used sequentially. So, the number of gates was minimized and SEED algorithm was fitted in FPGA without additional components. It was confirmed that the rate of resource usage is about 80% in ALTERA 10KE and the SEED design operates in a clock frequency of 131.57 MHz and an encryption rate of 29 Mbps.
In this paper we use Boolean models to generate new results in Combinatorics. On the one hand, th... more In this paper we use Boolean models to generate new results in Combinatorics. On the one hand, these new results answer real questions which have not been solved so far. On the other hand, these new results can immediately be useful for future applications. We emphasize a new sequence of numbers which we call, due to the analyzed problem, the sequence of Bishop numbers. It will also be very useful to study the methodology that has been applied. Any problem that can be converted into a Boolean model can be solved for a broad range of parameters in a constructive way. It is not only known that there are solutions, the results will be fully available. This relates particularly to all constraint-related problems, even when the Boolean models are very complex.
Proceedings of 1995 IEEE International Conference on Fuzzy Systems. The International Joint Conference of the Fourth IEEE International Conference on Fuzzy Systems and The Second International Fuzzy Engineering Symposium
The application of knowledge which can be considered only incompletely and imprecisely and the co... more The application of knowledge which can be considered only incompletely and imprecisely and the combination of this knowledge by means of evaluation functions results in uncertain values. In many search algorithms, this uncertainty simply is ignored by using only the resulting (crisp) value. It is assumed that the consideration of this uncertainty in search algorithms will give better results. The
Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94)
Page 1. Neural Network Learning in a Chess Endgame Christian Posthoff, Stanislaw Schawelski, Mich... more Page 1. Neural Network Learning in a Chess Endgame Christian Posthoff, Stanislaw Schawelski, Michael Schlosser Dept. ... These two chessmen are alone active during the play. For more details see [SCHLOSSER 921. Main results of this EDB construction (cf. [SCHLOSSER ...
Proceedings Intelligent Information Systems. IIS'97
The learning of propositional and fuzzy-logical functions and structures has been thoroughly expl... more The learning of propositional and fuzzy-logical functions and structures has been thoroughly explored in the past years and has become an efficient means for knowledge acquisition. Decision trees are broadly discussed and used, many algorithms for the learning of optimal decision trees are available. Publications and implementations, however, very often show a considerable lack of understanding of the capacities and
Algorithms for Games aims to provide a concrete example of the programming of a two-person game w... more Algorithms for Games aims to provide a concrete example of the programming of a two-person game with complete information, and to demonstrate some of the methods of solutions; to show the reader that it is profitable not to fear a search, but rather to undertake it in a rational fashion, make a proper estimate of the dimensions of the "catastrophe", and use all suitable means to keep it down to a reasonable size. The book is dedicated to the study of methods for limiting the extent of a search. The game programming problem is very well suited to the study of the search problem, and in general for multi-step solution processes. With this in mind, the book focuses on the programming of games as the best means of developing the ideas and methods presented. While many of the examples are related to chess, only an elementary knowledge of the game is needed.
This position statement provides guidelines for assessing risk associated with carotid endarterec... more This position statement provides guidelines for assessing risk associated with carotid endarterectomy and defines the point at which risk is too high to perform surgery for specific indications described below. Morbidity and mortality levels are discussed. This statement does not address indications for surgery or merits of specific medical or surgical treatments. Results of current studies that compare relative risk of various treatments for carotid artery disease are not yet available.
Abstract—This paper aims at the classiffication of bent functions in order to allow their constru... more Abstract—This paper aims at the classiffication of bent functions in order to allow their construction without searching or sieving. We focus on the characterization of bent functions in the context of Specialized Normal Forms. Furthermore we want to express bent functions in terms of derivative operations of the Boolean Differential Calculus. In order to solve these problems, we study bent functions of two and four variables in detail. This exploration leads finally to Boolean differential equations that will allow the direct calculation of bent functions. Keywords-bent function; classification; specialized normal form; Boolean Differential Calculus; Boolean differential equation; XBOOLE.
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Papers by Christian Posthoff