Related papers: Expressivity within second-order transitive-closur…
The characterization of PSPACE-queries over ordered structures as exactly those expressible in first-order logic with partial fixpoints (Vardi'82) is one of the classical results in the field of descriptive complexity. In this paper, we…
The SPARC TSO weak memory model is defined axiomatically, with a non-compositional formulation that makes modular reasoning about programs difficult. Our denotational approach uses pomsets to provide a compositional semantics capturing…
Logical transductions provide a very useful tool to encode classes of structures inside other classes of structures. In this paper we study first-order (FO) transductions and the quasiorder they induce on infinite classes of finite graphs.…
Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free…
We study the satisfiability problem for the two-variable first-order logic over structures with one transitive relation. % We show that the problem is decidable in 2-NExpTime for the fragment consisting of formulas where existential…
We investigate the expressive power of state space models (SSM), which have recently emerged as a potential alternative to transformer architectures in large language models. Building on recent work, we analyse SSM expressiveness through…
Algorithmic meta-theorems explain the tractability of large classes of computational problems by linking logical expressibility with structural graph properties. While extensions of first-order logic such as FO+dp admit efficient model…
We analyze the computational complexity of admissibility and unifiability with parameters in transitive modal logics. The class of cluster-extensible (clx) logics was introduced in the first part of this series of papers. We completely…
We prove that the equational theory of the positive calculus of relations with transitive closure (PCoR*) is EXPSPACE-complete. Here, PCoR* terms consist of the following standard operators on binary relations: identity, empty,…
We study an extension of FO^2[<], first-order logic interpreted in finite words, in which formulas are restricted to use only two variables. We adjoin to this language two-variable atomic formulas that say, `the letter a appears between…
Transitive closure logic is a known extension of first-order logic obtained by introducing a transitive closure operator. While other extensions of first-order logic with inductive definitions are a priori parametrized by a set of inductive…
In topological modal logic, it is well known that the Cantor derivative is more expressive than the topological closure, and the `elsewhere,' or `difference,' operator is more expressive than the `somewhere' operator. In 2014, Kudinov and…
It is natural that we can extend Structural Operational Semantics (SOS) to SOS for true concurrency. From SOS to SOS for true concurrency, it is in nature to give the related concepts in SOS a truly concurrent semantics foundation, i.e., a…
It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is equivalent to the recently introduced extended tensor type…
Temporal logic is a very powerful formalism deeply investigated and used in formal system design and verification. Its application usually reduces to solving specific decision problems such as model checking and satisfiability. In these…
The complexity class $NP$ can be logically characterized both through existential second order logic $SO\exists$, as proven by Fagin, and through simulating a Turing machine via the satisfiability problem of propositional logic SAT, as…
This paper presents a complete axiomatization of Monadic Second-Order Logic (MSO) over infinite trees. MSO on infinite trees is a rich system, and its decidability ("Rabin's Tree Theorem") is one of the most powerful known results…
Temporal logics are a powerful tool to specify properties of computational systems. For concurrent programs, Higher Dimensional Automata (HDA) are a very expressive model of non-interleaving concurrency. HDA recognize languages of partially…
Krebs et al. (2007) gave a characterization of the complexity class TC0 as the class of languages recognized by a certain class of typed monoids. The notion of typed monoid was introduced to extend methods of algebraic automata theory to…
Our concern is the problem of determining the data complexity of answering an ontology-mediated query (OMQ) formulated in linear temporal logic LTL over (Z,<) and deciding whether it is rewritable to an FO(<)-query, possibly with some extra…