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We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…
In recent years there has been considerable interest in theories over string equations, length function, and string-number conversion predicate within the formal verification, software engineering, and security communities. SMT solvers for…
This paper tackles the problem of the existence of solutions for recursive systems of Horn clauses with second-order variables interpreted as integer relations, and harnessed by quantifier-free difference bounds arithmetic. We start by…
We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types)…
String constraint solving refers to solving combinatorial problems involving constraints over string variables. String solving approaches have become popular over the last years given the massive use of strings in different application…
We study the computational complexity of short sentences in Presburger arithmetic (Short-PA). Here by "short" we mean sentences with a bounded number of variables, quantifiers, inequalities and Boolean operations; the input consists only of…
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…
We study linear-time temporal logics interpreted over data words with multiple attributes. We restrict the atomic formulas to equalities of attribute values in successive positions and to repetitions of attribute values in the future or…
We investigate the satisfiability and finite satisfiability problem for probabilistic computation-tree logic (PCTL) where operators are not restricted by any step bounds. We establish decidability for several fragments containing…
Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and…
Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which…
Satisfiability of boolean formulae (SAT) has been a topic of research in logic and computer science for a long time. In this paper we are interested in understanding the structure of satisfiable and unsatisfiable sentences. In previous work…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. Length constraints restrict valid substitutions of…
We study the computational complexity of model checking and satisfiability problems of polyadic modal logics extended with permutations and Boolean operators on accessibility relations. First, we show that the combined complexity of the…
We provide a constraint based computational model of linear precedence as employed in the HPSG grammar formalism. An extended feature logic which adds a wide range of constraints involving precedence is described. A sound, complete and…
Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…
The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics with branching types beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the coalgebraic $\mu$-calculus…