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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…
We investigate the domain of satisfiable formulas in satisfiability modulo theories (SMT), in particular, automatic generation of a multitude of satisfying assignments to such formulas. Despite the long and successful history of SMT in…
We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpretation of Q varies with the structures. The second result…
Recently, the separated fragment (SF) has been introduced and proved to be decidable. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. The known upper bound on the time…
The canonical class in the realm of counting complexity is #P. It is well known that the problem of counting the models of a propositional formula in disjunctive normal form (#DNF) is complete for #P under Turing reductions. On the other…
Quantified CTL (QCTL) extends the temporal logic CTL with quantifications over atomic propositions. This extension is known to be very expressive: QCTL allows us to express complex properties over Kripke structures (it is as expressive as…
Quantifier-free nonlinear arithmetic (QF_NRA) appears in many applications of satisfiability modulo theories solving (SMT). Accordingly, efficient reasoning for corresponding constraints in SMT theory solvers is highly relevant. We propose…
The constraint satisfaction problem, parameterized by a relational structure, provides a general framework for expressing computational decision problems. Already the restriction to the class of all finite structures forms an interesting…
This paper presents a complete algorithmic study of the decision Boolean Satisfiability Problem under the classical computation and quantum computation theories. The paper depicts deterministic and probabilistic algorithms, propositions of…
Incremental SAT and QBF solving potentially yields improvements when sequences of related formulas are solved. An incremental application is usually tailored towards some specific solver and decomposes a problem into incremental solver…
The notion of functional dependencies (FDs) can be used by data scientists and domain experts to confront background knowledge against data. To overcome the classical, too restrictive, satisfaction of FDs, it is possible to replace equality…
The Boolean Satisfiability (SAT) problem is the canonical NP-complete problem and is fundamental to computer science, with a wide array of applications in planning, verification, and theorem proving. Developing and evaluating practical SAT…
Generalised Satisfiability Problems (or Boolean Constraint Satisfaction Problems), introduced by Schaefer in 1978, are a general class of problem which allow the systematic study of the complexity of satisfiability problems with different…
We demonstrate a family of propositional formulas in conjunctive normal form so that a formula of size $N$ requires size $2^{\Omega(\sqrt[7]{N/logN})}$ to refute using the tree-like OBDD refutation system of Atserias, Kolaitis and Vardi…
Differential-algebraic equations (DAEs) arise in power networks, chemical processes, and multibody systems, where algebraic constraints encode physical conservation laws. The safety of such systems is critical, yet safe control is…
QBFs (quantified boolean formulas), which are a superset of propositional formulas, provide a canonical representation for PSPACE problems. To overcome the inherent complexity of QBF, significant effort has been invested in developing QBF…
We call a CNF formula linear if any two clauses have at most one variable in common. Let Linear k-SAT be the problem of deciding whether a given linear k-CNF formula is satisfiable. Here, a k-CNF formula is a CNF formula in which every…
This article presents a technique for proving problems hard for classes of the polynomial hierarchy or for PSPACE. The rationale of this technique is that some problem restrictions are able to simulate existential or universal quantifiers.…
Satisfiability (SAT) is a central problem in computer science, and advances in SAT-solving algorithms have a far-reaching impact across many fields. Recent works have proposed quantum SAT solvers based on Grover's algorithm, a quantum…
The study of SAT and its variants has provided numerous NP-complete problems, from which most NP-hardness results were derived. Due to the NP-hardness of SAT, adding constraints to either specify a more precise NP-complete problem or to…