Related papers: The DFAs of Finitely Different Languages

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…

Regular expressions (res), because of their succinctness and clear syntax, are the common choice to represent regular languages. However, efficient pattern matching or word recognition depend on the size of the equivalent nondeterministic…

A filtration of a formal language L by a sequence s maps L to the set of words formed by taking the letters of words of L indexed only by s. We consider the languages resulting from filtering by all arithmetic progressions. If L is regular,…

We approximate functionals depending on the gradient of $u$ and on the behaviour of $u$ near the discontinuity points, by families of non-local functionals where the gradient is replaced by finite differences. We prove pointwise…

A two-way deterministic finite state automaton with one counter (2D1CA) is a fundamental computational model that has been examined in many different aspects since sixties, but we know little about its power in the case of unary languages.…

We give bounds on the number of distinct differences $N_a-a$ as $a$ varies over all elements of a given finite set $A$, and $N_a$ is a nearest neighbour to $a$.

Let $NFA_b(q)$ denote the set of languages accepted by nondeterministic finite automata with $q$ states over an alphabet with $b$ letters. Let $B_n$ denote the set of words of length $n$. We give a quadratic lower bound on the VC dimension…

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 establish a Myhill-Nerode type theorem for higher-dimensional automata (HDAs), stating that a language is regular if and only if it has finite prefix quotient. HDAs extend standard automata with additional structure, making it possible…

We define two finite q-analogs of certain multiple harmonic series with an arbitrary number of free parameters, and prove identities for these q-analogs, expressing them in terms of multiply nested sums involving the Gaussian binomial…

The automation of decision procedures makes certification essential. We suggest to use determinacy of turn-based two-player games with regular winning conditions in order to generate certificates for the number of states that a…

We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language -- the input of the problem -- and fixed language called filter is non-empty. We consider two kind of…

The theory of abstract argumentation frameworks (afs) has, in the main, focused on finite structures, though there are many significant contexts where argumentation can be regarded as a process involving infinite objects. To address this…

We show that a well-known family of deterministic finite automata can be used to distinguish distinct binary strings of the same length from every start state. Further, we establish almost matching lower and upper bounds on the number of…

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…

Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…

An automaton is unambiguous if for every input it has at most one accepting computation. An automaton is k-ambiguous (for k > 0) if for every input it has at most k accepting computations. An automaton is boundedly ambiguous if it is…

Four problems related to information divergence measures defined on finite alphabets are considered. In three of the cases we consider, we illustrate a contrast which arises between the binary-alphabet and larger-alphabet settings. This is…

We study the class of languages that have membership proofs which can be verified by real-time finite-state machines using only a constant number of random bits, regardless of the size of their inputs. Since any further restriction on the…

We study the problems of finding a shortest synchronizing word and its length for a given prefix code. This is done in two different settings: when the code is defined by an arbitrary decoder recognizing its star and when the code is…