形式语言与自动机理论

Given an integer base $b>1$, a set of integers is represented in base $b$ by a language over $\{0,1,...,b-1\}$. The set is said to be $b$-recognisable if its representation is a regular language. It is known that eventually periodic sets…

The purpose of the present paper is to show that: Eilenberg-type correspondences = Birkhoff's theorem for (finite) algebras + duality. We consider algebras for a monad T on a category D and we study (pseudo)varieties of T-algebras.…

We present a new series of examples of binary slowly synchronizing automata with sink state. The reset threshold of the $n$-state automaton in this series is $\frac{n^2}{4}+2n-9$. This improves on the previously known lower bound for the…

Context-free and context-sensitive formal grammars are often regarded as more appropriate to model proteins than regular level models such as finite state automata and Hidden Markov Models. In theory, the claim is well founded in the fact…

We show that equivalence of deterministic top-down tree-to-string transducers is decidable, thus solving a long standing open problem in formal language theory. We also present efficient algorithms for subclasses: polynomial time for total…

We tackle the problem of simultaneous transformations of networks represented as graphs. Roughly speaking, one may distinguish two kinds of simultaneous or parallel rewrite relations over complex structures such as graphs: (i) those which…

We show how up-to techniques for (bi-)similarity can be used in the setting of weighted systems. The problems we consider are language equivalence, language inclusion and the threshold problem (also known as universality problem) for…

Two words $w_1$ and $w_2$ are said to be $k$-binomial equivalent if every non-empty word $x$ of length at most $k$ over the alphabet of $w_1$ and $w_2$ appears as a scattered factor of $w_1$ exactly as many times as it appears as a…

Weighted automata (WA) are an important formalism to describe quantitative properties. Obtaining equivalent deterministic machines is a longstanding research problem. In this paper we consider WA with a set semantics, meaning that the…

In this paper, we propose a novel algorithm to learn a B\"uchi automaton from a teacher who knows an $\omega$-regular language. The algorithm is based on learning a formalism named family of DFAs (FDFAs) recently proposed by Angluin and…

A regular language $L$ is non-returning if in the minimal deterministic finite automaton accepting it there are no transitions into the initial state. Eom, Han and Jir\'askov\'a derived upper bounds on the state complexity of boolean…

We study descriptive complexity properties of the class of regular bifix-free languages, which is the intersection of prefix-free and suffix-free regular languages. We show that there exist a single ternary universal (stream of) bifix-free…

The state complexity of a regular language is the number of states in a minimal deterministic finite automaton accepting the language. The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The…

We consider the problems of liveness verification and liveness synthesis for recursive programs. The liveness verification problem (LVP) is to decide whether a given omega-context-free language is contained in a given omega-regular…

Functional transductions realized by two-way transducers (equivalently, by streaming transducers and by MSO transductions) are the natural and standard notion of "regular" mappings from words to words. It was shown recently (LICS'13) that…

In this paper we study the logical aspects of branching automata, as defined by Lodaya and Weil. We first prove that the class of languages of finite N-free posets recognized by branching automata is closed under complementation. Then we…

The value 1 problem is a decision problem for probabilistic automata over finite words: given a probabilistic automaton, are there words accepted with probability arbitrarily close to 1? This problem was proved undecidable recently; to…

The notion of orbit finite data monoid was recently introduced by Bojanczyk as an algebraic object for defining recognizable languages of data words. Following Buchi's approach, we introduce a variant of monadic second-order logic with data…

Given two languages, a separator is a third language that contains the first one and is disjoint from the second one. We investigate the following decision problem: given two regular input languages of finite words, decide whether there…

A weighted automaton is functional if any two accepting runs on the same finite word have the same value. In this paper, we investigate functional weighted automata for four different measures: the sum, the mean, the discounted sum of…