Information Processing Letters

Glaßer et al. (SIAMJCOMP 2009 and TCS 2009) proved that NP-complete languages are polynomial-time mitotic for the many-one reduction, meaning that each NP-complete language L can be split into two NP-complete languages L ∩ S and L ∩ S ‾, where S ...

• Every NP-complete (NPC) set can be partitioned into infinitely many NPC subsets.
• Every NPC set can be partitioned into an effectively presentable infinite set of NPC subsets.
• Every NPC set can be partitioned into infinitely many ...

We study a robust single-machine scheduling problem with uncertain processing times on a serial-batch processing machine to minimize maximum lateness. The problem can model many practical production and logistics applications which involve ...

• We study robust scheduling to minimize maximum lateness with uncertain processing times on a serial-batch processing machine.
• Two algorithms are designed to evaluate the maximum lateness when a solution is given.
• We design an ...

Recently we established an analog of Gabbay's separation theorem about linear temporal logic (LTL) for the extension of Moszkowski's discrete time propositional Interval Temporal Logic (ITL) by two sets of expanding modalities, namely the unary ...

• Recently we established temporal separation for the extension of Moszkowski's discrete time ITL by the neighbourhood modalities.
• We show how temporal separation for ITL by the neighbourhood modalities facilitates a proof of this system'...

We consider the following Markov Reachability decision problems that view Markov Chains as Linear Dynamical Systems: given a finite, rational Markov Chain, source and target states, and a rational threshold, does the probability of reaching the ...

• We consider reachability problems that view Markov Chains as Linear Dynamical Systems (LDS).
• We reduce number-theoretically hard problems for Linear Recurrence Sequences (LRS) to Markov Reachability Problems.
• We map LRS of order k ...

The graph searches Breadth First Search (BFS) and Depth First Search (DFS) and the spanning trees constructed by them are some of the most basic concepts in algorithmic graph theory. BFS trees are first-in trees, i.e., every vertex is connected ...

• NP-completeness of last-in search tree recognition for trees of bounded height.
• Tightness proof for the height bound by presenting polynomial-time algorithm for trees with small height.
• Improved running time for search tree ...

We study the sample complexity of learning ReLU neural networks from the point of view of generalization. Given norm constraints on the weight matrices, a common approach is to estimate the Rademacher complexity of the associated function class. ...

• An improved generalization bound for neural networks is established.
• The analysis highlights a new way to recursively apply Talagrand's contraction principle.
• The proof is extremely short.

We study public goods games, a type of game where every player has to decide whether or not to produce a good which is public, i.e., neighboring players can also benefit from it. Specifically, we consider a setting where the good is indivisible ...

• We consider public goods games with indivisible goods on directed graphs.
• We show that computing any non-trivial approximate mixed Nash equilibrium is PPAD-hard.
• This is shown by a direct reduction from the Pure-Circuit problem.

We show that every prenex universal syntactic first-order safety property can be compiled into a universal invariant of a first-order transition system using quantifier-free substitutions only. We apply this insight to prove that every such ...

• FO linear temporal logic allows to specify temporal properties of parametric systems given by FO transition systems.
• For syntactic safety formulas in prenex form with universal quantifiers only, we show how to reduce checking safety of ...

With the development of Lie theory, Lie groups have profound significance in many branches of mathematics and physics. In Lie theory, matrix exponential plays a crucial role between Lie groups and Lie algebras. Meanwhile, as finite analogues of ...

• We built the relationship between matrix exponential and discrete logarithmic problem (DLP) in finite groups of Lie type.
• We proved that the complexity of solving non-abelian factorization (NAF) problem in finite groups of Lie type is ...

Given a universe U = R ∪ B of a finite set of red elements R, and a finite set of blue elements B and a family F of subsets of U, the Red Blue Set Cover problem is to find a subset F ′ of F that covers all blue elements of B and minimum number of ...

• Given universe U = R ∪ B, red set R, blue set B, and family F, solve Red Blue Set Cover: find F ′ ⊆ F covering all B with minimal R.
• We prove that the RBSC problem is NP-hard even when R and B in IR 2 and the sets in F are defined by ...

Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs in ...

• We prove that regular resolution effectively simulates resolution.
• We prove that regular resolution is not closed under substitutions.
• We reprove a recent result on the hardness of automating regular resolution.

We propose a framework for speeding up maximum flow computation by using predictions. A prediction is a flow, i.e., an assignment of non-negative flow values to edges, which satisfies the flow conservation property, but does not necessarily ...

• We speed up maximum flow computation in graphs by using predictions.
• Prediction is a flow satisfying flow conservation but not necessarily capacities.
• We show that such predictions are efficiently learnable.
• We compute flow in ...

The seminal work of Charikar et al. [1] called Count-Sketch suggests a sketching algorithm for real-valued vectors that has been used in frequency estimation for data streams and pairwise inner product estimation for real-valued vectors etc. One ...

• In this work we propose a sketching algorithm called Sparse Count Sketch (SCS).
• It efficiently estimates the inner-product and frequency of streaming datasets.
• It offers a sparser sketch along with faster running time than vanilla ...

The qCCS model proposed by Feng et al. provides a powerful framework to describe and reason about quantum communication systems that could be entangled with the environment. However, they only studied weak bisimulation semantics. In this paper we ...

• A new branching bisimilarity for quantum CCS has been proposed based on the notion of ϵ-tree.
• This bisimilarity has been shown to be a congruence relation.
• An efficient verification algorithm for the ground version of our branching ...

In the Longest ( s , t ) -Detour problem, we look for an ( s , t )-path that is at least k vertices longer than a shortest one. We study the parameterized complexity of Longest ( s , t ) -Detour when parameterized by k: this falls into the ...

• In Longest ( s , t )-Detour problem, we look for an ( s , t )-path that is at least k vertices longer than a shortest one.
• We study Longest ( s , t )-Detour when parameterized by k: this falls into the paradigm of ‘parameterization ...

In this paper we consider two vertex deletion problems. In the Block Vertex Deletion problem, the input is a graph G and an integer k, and the goal is to decide whether there is a set of at most k vertices whose removal from G result in a block ...

• We study two vertex deletion problems: Block Vertex Deletion and Pathwidth One Vertex Deletion.
• We give a better analysis of the kernel for Block Vertex Deletion of Agrawal el al. (LATIN 2016).
• We give a kernel for Pathwidth One ...

Recently, a class of quaternary sequences with period pq, where p and q are two distinct odd primes introduced by Zhang et al. were proved to possess high linear complexity and 4-adic complexity. In this paper, we determine the autocorrelation ...

We study the problem of computing the center of cycle graphs whose vertices are weighted. The distance from a vertex to a point of the graph is defined as the weight of the vertex times the length of the shortest path between the vertex and the ...

• We give an O ( n )-time algorithm for the discrete and continuous weighted center problem on cycle graphs with n vertices. Our algorithm improves upon the best known algorithm by Rayco et al. that takes O ( n log ⁡ n ) time.
• For a ...

Let A, B, and C be three n × n matrices. We investigate the problem of verifying whether A B = C over the ring of integers and finding the correct product AB. Given that C is different from AB by at most k entries, we propose an algorithm that ...

• A simple combinatorial algorithm for correcting integer matrix products.
• Detecting erroneous entries by combinatorial group testing.
• Integers used in the computation are polynomial bounded in the input value and size.