Related papers: A Decision Problem for Ultimately Periodic Sets in…
We show that many classical decision problems about 1-counter omega-languages, context free omega-languages, or infinitary rational relations, are $\Pi_2^1$-complete, hence located at the second level of the analytical hierarchy, and…
Finite-state tree automata are a well studied formalism for representing term languages. This paper studies the problem of determining the regularity of the set of instances of a finite set of terms with variables, where each variable is…
In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…
We investigate binary voting systems with two types of voters and a hierarchy among the members in each type, so that members in one class have more influence or importance than members in the other class. The purpose of this paper is to…
Students find their first course in Formal Languages and Automata Theory challenging. In addition to the development of formal arguments, most students struggle to understand nondeterministic computation models. In part, the struggle stems…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
Altenbernd, Thomas and W\"ohrle have considered in [ATW02] acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the B\"uchi and Muller ones,…
The termination problem for affine programs over the integers was left open in\cite{Braverman}. For more that a decade, it has been considered and cited as a challenging open problem. To the best of our knowledge, we present here the most…
In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…
Automata over infinite alphabets have emerged as a convenient computational model for processing structures involving data, such as nonces in cryptographic protocols or data values in XML documents. We introduce active learning methods for…
Register automata are finite automata equipped with a finite set of registers ranging over the domain of some relational structure like $(\mathbb N;=)$ or $(\mathbb Q;<)$. Register automata process words over the domain, and along a run of…
This is a survey on the finite basis problem for varieties of algebraic systems. Our exposition is in two directions: (i) We give numerous examples of varieties which are not finitely based. (ii) We give examples of important varieties with…
We study the language universality problem for One-Counter Nets, also known as 1-dimensional Vector Addition Systems with States (1-VASS), parameterized either with an initial counter value, or with an upper bound on the allowed counter…
Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member…
Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical…
In this paper we consider a number of natural decision problems involving k-regular sequences. Specifically, they arise from - lower and upper bounds on growth rate; in particular boundedness, - images, - regularity (recognizability by a…
Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of…
A two-dimensional finite automaton has a read-only input head that moves in four directions on a finite array of cells labelled by symbols of the input alphabet. A three-way two-dimensional automaton is prohibited from making upward moves,…
We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…
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…