Related papers: Coalgebraic Satisfiability Checking for Arithmetic…
Labelled tableaux have been a traditional approach to define satisfiability checking procedures for Modal Logics. In many cases, they can also be used to obtain tight complexity bounds and lead to efficient implementations of reasoning…
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…
Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…
The satisfiability problem for branching-time temporal logics like CTL*, CTL and CTL+ has important applications in program specification and verification. Their computational complexities are known: CTL* and CTL+ are complete for doubly…
Concrete domains, especially those that allow to compare features with numeric values, have long been recognized as a very desirable extension of description logics (DLs), and significant efforts have been invested into adding them to usual…
Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is…
Rational verification refers to the problem of checking which temporal logic properties hold of a concurrent multiagent system, under the assumption that agents in the system choose strategies that form a game-theoretic equilibrium.…
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…
Word-level verification of arithmetic circuits with large operands typically relies on arbitrary-precision arithmetic, which can lead to significant computational overhead as word sizes grow. In this paper, we present a hybrid algebraic…
The complexity of a computational problem is traditionally quantified based on the hardness of its worst case. This approach has many advantages and has led to a deep and beautiful theory. However, from the practical perspective, this…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
In order to prove that the P of problems is different to the NP class, we consider the satisfability problem of propositional calculus formulae, which is an NP-complete problem. It is shown that, for every search algorithm A, there is a set…
We investigate the complexity consequences of adding pointer arithmetic to separation logic. Specifically, we study extensions of the points-to fragment of symbolic-heap separation logic with various forms of Presburger arithmetic…
Consider a multi-class labelling problem, where the labels can take values in $[k]$, and a predictor predicts a distribution over the labels. In this work, we study the following foundational question: Are there notions of multi-class…
We present CLTLB(D), an extension of PLTLB (PLTL with both past and future operators) augmented with atomic formulae built over a constraint system D. Even for decidable constraint systems, satisfiability and Model Checking problem of such…
These notes contain, among others, a proof that the average running time of an easy solution to the satisfiability problem for propositional calculus is, under some reasonable assumptions, linear (with constant 2) in the size of the input.…
We introduce and investigate the expressive description logic (DL) ALCSCC++, in which the global and local cardinality constraints introduced in previous papers can be mixed. On the one hand, we prove that this does not increase the…
We initiate the study of parameterized complexity of $\textsf{QMA}$ problems in terms of the number of non-Clifford gates in the problem description. We show that for the problem of parameterized quantum circuit satisfiability, there exists…
We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include \begin{romannum} \item[{}] {\sc 3Sat, 1-3Sat, 1-Ex3Sat,…
The aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The…