Related papers: A Decision Procedure for String Logic with Equatio…
We consider the satisfiability problem for the two-variable fragment of the first-order logic extended with modulo counting quantifiers and interpreted over finite words or trees. We prove a small-model property of this logic, which gives a…
Interval temporal logics provide a natural framework for qualitative and quantitative temporal reason- ing over interval structures, where the truth of formulae is defined over intervals rather than points. In this paper, we study the…
We solve the satisfiability problem for a three-sorted fragment of set theory (denoted $3LQST_0^R$), which admits a restricted form of quantification over individual and set variables and the finite enumeration operator $\{\text{-},…
We study the satisfiability of randomly generated formulas formed by $M$ clauses of exactly $K$ literals over $N$ Boolean variables. For a given value of $N$ the problem is known to be most difficult with $\alpha=M/N$ close to the…
We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…
We identify a fragment of Presburger arithmetic enriched with free function symbols and cardinality constraints for interpreted sets, which is amenable to automated analysis. We establish decidability and complexity results for such a…
To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings,…
First-order predicate logic extended with linear arithmetic is undecidable, in general. We show that the Bernays-Sch\"onfinkel-Ramsey (BSR) fragment extended with linear arithmetic restricted to simple bounds (SB) is decidable through…
We study algorithms for solving three problems on strings. The first one is the Most Frequently String Search Problem. The problem is the following. Assume that we have a sequence of $n$ strings of length $k$. The problem is finding the…
We present an approach to parameterized reachability for communicating finite-state threads that formulates the analysis as a satisfiability problem. In addition to the unbounded number of threads, the main challenge for SAT/SMT-based…
We consider the almost-sure (a.s.) termination problem for probabilistic programs, which are a stochastic extension of classical imperative programs. Lexicographic ranking functions provide a sound and practical approach for termination of…
We study the finitary satisfiability problem for first order logic with two variables and two binary relations, corresponding to the induced successor relations of two finite linear orders. We show that the problem is decidable in NEXPTIME.
Requirements over strings, commonly represented using natural language (NL), are particularly relevant for software systems due to their heavy reliance on string data manipulation. While individual requirements can usually be analyzed…
We refine the formulation of the Boolean satisfiability problem with $n$ Boolean variables in Clifford algebra ${\cal C}\ell(\mathbb{R}^{n,n})$ [3] and exploit this continuous setting to outline a new unsatisfiability test. This algorithm…
One of the long-standing research problems on logic programming is to treat the cut predicate in a logical, high-level way. We argue that this problem can be solved by adopting linear logic and choice-disjunctive goal formulas of the form…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…
String constraint solving, and the underlying theory of word equations, are highly interesting research topics both for practitioners and theoreticians working in the wide area of satisfiability modulo theories. As string constraint solving…
We show that strict deterministic propositional dynamic logic with intersection is highly undecidable, solving a problem in the Stanford Encyclopedia of Philosophy. In fact we show something quite a bit stronger. We introduce the…
We introduce the task of out-of-order membership to a formal language L, where the letters of a word w are revealed one by one in an adversarial order. The length |w| is known in advance, but the content of w is streamed as pairs (i, w[i]),…
Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random…