Related papers: Deciding FO-definability of regular languages

The circuit complexity class DLOGTIME-uniform AC^0 is known to be a modest subclass of DLOGTIME-uniform TC^0. The weakness of AC^0 is caused by the fact that AC^0 is not closed under restricting AC^0-computable queries into simple…

We study property testing of properties that are definable in first-order logic (FO) in the bounded-degree graph and relational structure models. We show that any FO property that is defined by a formula with quantifier prefix…

We introduce a new setting, the category of $\omega$PAP spaces, for reasoning denotationally about expressive differentiable and probabilistic programming languages. Our semantics is general enough to assign meanings to most practical…

The problem if a given configuration of a pushdown automaton (PDA) is bisimilar with some (unspecified) finite-state process is shown to be decidable. The decidability is proven in the framework of first-order grammars, which are given by…

One of the most interesting questions concerning hierarchical control of discrete-event systems with partial observations is a condition under which the language observability is preserved between the original and the abstracted plant.…

There are many different semantics for general logic programs (i.e. programs that use negation in the bodies of clauses). Most of these semantics are Turing complete (in a sense that can be made precise), implying that they are undecidable.…

For an ordinal $\lambda>0$, we use the Erd\H{o}s--Rado partition theorem to prove the failure of strong completeness of $\mathsf{GL}$ for modal languages of cardinality $(2^{|\lambda|+\aleph_0})^{+}$ with respect to models on ordinals…

We show that deciding boundedness (aka FO-rewritability) of monadic single rule datalog programs (sirups) is 2Exp-hard, which matches the upper bound known since 1988 and finally settles a long-standing open problem. We obtain this result…

Building upon the known generalized-quantifier-based first-order characterization of LOGCFL, we lay the groundwork for a deeper investigation. Specifically, we examine subclasses of LOGCFL arising from varying the arity and nesting of…

We show a number of undecidable assertions concerning countably compact spaces hold under PFA(S)[S]. We also show the consistency without large cardinals of "every locally compact, perfectly normal space is paracompact".

The purpose of this paper is to provide efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbidden-chain…

We introduce fixpoint definitions, a rule-based reformulation of fixpoint constructs. The logic FO(FD), an extension of classical logic with fixpoint definitions, is defined. We illustrate the relation between FO(FD) and FO(ID), which is…

We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…

We give a necessary and sufficient condition for a one-dimensional regular and Hausdorff topological space definable in a definably complete uniformly locally o-minimal structure of the second kind having definable bounded multiplication…

A DFA $\mathcal{A}$ is composite if there exist DFAs $\mathcal{A}_1,\dots,\mathcal{A}_t$ with $\mathcal{L}(\mathcal{A}) = \bigcap_{i=1}^{t} \mathcal{L}(\mathcal{A}_i)$ such that each $\mathcal{A}_i$ has strictly less states than the minimal…

We investigate the intersection problem for finite monoids, which asks for a given set of regular languages, represented by recognizing morphisms to finite monoids from a variety V, whether there exists a word contained in their…

Uniform one-dimensional fragment UF1^= is a formalism obtained from first-order logic by limiting quantification to applications of blocks of existential (universal) quantifiers such that at most one variable remains free in the quantified…

Many logical properties are known to be undecidable for normal modal logics, with few exceptions such as consistency and coincidence with $\mathsf{K}$. This paper shows that the property of being a union-splitting in…

Logical formalisms such as first-order logic (FO) and fixpoint logic (FP) are well suited to express in a declarative manner fundamental graph functionalities required in distributed systems. We show that these logics constitute good…

We will prove bi-interpretability of the arithmetic $\N = \langle N, +,\cdot, 0, 1\rangle$ and the weak second order theory of $\N$ with the free monoid $\mathbb{M}_X$ of finite rank greater than 1 and with a non-trivial partially…