Related papers: Deterministic Logics for UL
In temporal logics, a central question is about the choice of modalities and their relative expressive power, in comparison to the complexity of decision problems such as satisfiability. In this tutorial, we will illustrate the study of…
For a class L of languages let PDL[L] be an extension of Propositional Dynamic Logic which allows programs to be in a language of L rather than just to be regular. If L contains a non-regular language, PDL[L] can express non-regular…
A regular language $L$ is union-free if it can be represented by a regular expression without the union operation. A union-free language is deterministic if it can be accepted by a deterministic one-cycle-free-path finite automaton; this is…
We study the positive logic FO+ on finite words, and its fragments, pursuing and refining the work initiated in [Kuperberg 2023]. First, we transpose notorious logic equivalences into positive first-order logic: FO+ is equivalent to LTL+ ,…
We prove that, similarly to known PSpace-completeness of recognising FO(<)-definability of the language L(A) of a DFA A, deciding both FO(<,C)- and FO(<,MOD)-definability are PSpace-complete. (Here, FO(<,C) extends the first-order logic…
In this paper a conditional logic is defined and studied. This conditional logic, Deterministic Bayesian Logic, is constructed as a deterministic counterpart to the (probabilistic) Bayesian conditional. The logic is unrestricted, so that…
We define a class of languages of infinite words over infinite alphabets, and the corresponding automata. The automata used for recognition are a generalisation of deterministic Muller automata to the setting of nominal sets. Remarkably,…
We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…
We consider the class of languages defined in the 2-variable fragment of the first-order logic of the linear order. Many interesting characterizations of this class are known, as well as the fact that restricting the number of quantifier…
Partially ordered nondeterminsitic finite automata (poNFAs) are NFAs whose transition relation induces a partial order on states, that is, for which cycles occur only in the form of self-loops on a single state. A poNFA is universal if it…
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 give in this paper a logical characterization for unambiguous Context Free Languages, in the vein of descriptive complexity. A fragment of the logic characterizing context free languages given by Lautemann, Schwentick and Th\'erien [18]…
This paper studies the complexity of operations on finite automata and the complexity of their decision problems when the alphabet is unary. Let $n$ denote the maximum of the number of states of the input finite automata considered in the…
We show the surprising result that the cutpoint isolation problem is decidable for Probabilistic Finite Automata (PFA) where input words are taken from a letter-bounded context-free language. A context-free language $\mathcal{L}$ is…
Unambiguous non-deterministic finite automata have intermediate expressive power and succinctness between deterministic and non-deterministic automata. It has been conjectured that every unambiguous non-deterministic one-way finite…
We give topological and algebraic characterizations as well as language theoretic descriptions of the following subclasses of first-order logic FO[<] for omega-languages: Sigma_2, FO^2, the intersection of FO^2 and Sigma_2, and Delta_2 (and…
We investigate the expressive power of regular expressions for languages of countable words and establish their expressive equivalence with logical and algebraic characterizations. Our goal is to extend the classical theory of regular…
Model checking linear-time properties expressed in first-order logic has non-elementary complexity, and thus various restricted logical languages are employed. In this paper we consider two such restricted specification logics, linear…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
In this paper we consider the class of lambda-nondeterministic linear automata as a model of the class of linear languages. As usual in other automata models, lambda-moves do not increase the acceptance power. The main contribution of this…