相关论文: Complexity of Propositional Proofs under a Promise

We address lower bounds on the time complexity of algorithms solving the propositional satisfiability problem. Namely, we consider two DPLL-type algorithms, enhanced with the unit clause and pure literal heuristics. Exponential lower bounds…

As a natural extension of the SAT problem, an array of proof systems for quantified Boolean formulas (QBF) have been proposed, many of which extend a propositional proof system to handle universal quantification. By formalising the…

In 2003, Atserias and Dalmau resolved a major open question about the resolution proof system by establishing that the space complexity of CNF formulas is always an upper bound on the width needed to refute them. Their proof is beautiful…

DPLL and resolution are two popular methods for solving the problem of propositional satisfiability. Rather than algorithms, they are families of algorithms, as their behavior depend on some choices they face during execution: DPLL depends…

The CSP (constraint satisfaction problems) is a class of problems deciding whether there exists a homomorphism from an instance relational structure to a target one. The CSP dichotomy is a profound result recently proved by Zhuk (2020, J.…

We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions and iterated connectives ranging over intervals parameterized by arithmetic variables. The satisfiability problem is shown…

The fixed template Promise Constraint Satisfaction Problem (PCSP) is a recently proposed significant generalization of the fixed template CSP, which includes approximation variants of satisfiability and graph coloring problems. All the…

Many satisfiability modulo theories solvers implement a variant of the DPLL(T ) framework which separates theory-specific reasoning from reasoning on the propositional abstraction of the formula. Such solvers conclude that a formula is…

By considering probability distributions over the set of assignments the expected truth values assignment to propositional variables are extended through linear operators, and the expected truth values of the clauses at any given…

Limits on the number of satisfying assignments for CNS instances with n variables and m clauses are derived from various inequalities. Some bounds can be calculated in polynomial time, sharper bounds demand information about the…

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…

We intend to create new concepts aimed at finding necessary and sufficient conditions for Boolean satisfiability so that these conditions can be verified in polynomial time. Based on these conditions it will be possible to create an…

In recent years much effort was put into developing polynomial-time conditional lower bounds for algorithms and data structures in both static and dynamic settings. Along these lines we suggest a framework for proving conditional lower…

We consider logic-based argumentation in which an argument is a pair (Fi,al), where the support Fi is a minimal consistent set of formulae taken from a given knowledge base (usually denoted by De) that entails the claim al (a formula). We…

We consider Proof Complexity in light of the unusual binary encoding of certain combinatorial principles. We contrast this Proof Complexity with the normal unary encoding in several refutation systems, based on Resolution and Integer Linear…

In order to verify programs or hybrid systems, one often needs to prove that certain formulas are unsatisfiable. In this paper, we consider conjunctions of polynomial inequalities over the reals. Classical algorithms for deciding these not…

Proving proof-size lower bounds for $\mathbf{LK}$, the sequent calculus for classical propositional logic, remains a major open problem in proof complexity. We shed new light on this challenge by isolating the power of structural rules,…

In this paper, we analyze 2CNF formulas from the perspectives of Read-Once resolution (ROR) refutation schemes. We focus on two types of ROR refutations, viz., variable-once refutation and clause-once refutation. In the former, each…

We investigate the complexity of the satisfiability problem for a modal logic expressing `knowing how' assertions, related to an agent's abilities to achieve a certain goal. We take one of the most standard semantics for this kind of logics…

This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterised by a finite set F of non-negative functions that…