Related papers: The Complexity of Enriched Mu-Calculi
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…
Complementation of nondeterministic B\"uchi automata (BAs) is an important problem in automata theory with numerous applications in formal verification, such as termination analysis of programs, model checking, or in decision procedures of…
We investigate the expressivity and computational complexity of two modal logics on finite forests equipped with operators to reason on submodels. The logic ML(|) extends the basic modal logic ML with the composition operator | from static…
We define a new subclass of nondeterministic finite automata for prefix-closed languages called Flanked Finite Automata (FFA). We show that this class enjoys good complexity properties while preserving the succinctness of nondeterministic…
This paper explores the computational complexity of various natural one-variable fragments of first-order modal logics with the addition of counting quantifiers, over both constant and varying domains. The addition of counting quantifiers…
The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in…
In this paper, we consider iterative propositional calculi, which are finite sets of propositional formulas together with the rules of modus ponens and weak substitution (when formula being substituted must be already inferred). We…
We give an exact characterization of the computational complexity of the $k$CFA hierarchy. For any $k > 0$, we prove that the control flow decision problem is complete for deterministic exponential time. This theorem validates empirical…
We show that the emptiness (unsatisfiability) problem is undecidable and $\mathrm{\Pi}^{0}_{1}$-complete for deterministic propositional while programs with (graph) loop. To this end, we introduce a hypothesis elimination using loops. Using…
This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two…
The Triguarded Fragment (TGF) is among the most expressive decidable fragments of first-order logic, subsuming both its two-variable and guarded fragments without equality. We show that the TGF has the finite model property (providing a…
We present counting reward automata-a finite state machine variant capable of modelling any reward function expressible as a formal language. Unlike previous approaches, which are limited to the expression of tasks as regular languages, our…
Reasoning with defeasible and conflicting knowledge in an argumentative form is a key research field in computational argumentation. Reasoning under various forms of uncertainty is both a key feature and a challenging barrier for automated…
This paper shows, in the framework of the logical method,the unsolvability of $k$-set agreement task by devising a suitable formula of epistemic logic. The unsolvability of $k$-set agreement task is a well-known fact, which is a direct…
Quantifying the predictive uncertainty emerged as a possible solution to common challenges like overconfidence or lack of explainability and robustness of deep neural networks, albeit one that is often computationally expensive. Many…
We consider decision problems for relations over finite and infinite words defined by finite automata. We prove that the equivalence problem for binary deterministic rational relations over infinite words is undecidable in contrast to the…
We show that many classical decision problems about 1-counter omega-languages, context free omega-languages, or infinitary rational relations, are $\Pi_2^1$-complete, hence located at the second level of the analytical hierarchy, and…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
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…
Temporal logics for the specification of information-flow properties are able to express relations between multiple executions of a system. The two most important such logics are HyperLTL and HyperCTL*, which generalise LTL and CTL* by…