It is known that a language of finite words is definable in monadic second-order logic – MSO – (resp. first-order logic – FO –) iff it is recognized by some finite automaton (resp. some aperiodic finite automaton). Deciding whether an automaton A is equivalent to an aperiodic one is known to be PSPACE-complete. This problem has an important application in logic: it allows one to decide whether ...

ion Refinement and Antichains for Trace Inclusion of Infinite State Systems Radu Iosif, Adam Rogalewicz, and Tomáš Vojnar CNRS/Verimag, France and FIT BUT, Czech Republic Abstract. A data automaton is a finite automaton equipped with variables (counA data automaton is a finite automaton equipped with variables (counters or registers) ranging over infinite data domains. A trace of a data automat...

We present in this paper a methodology how to use 'Parallel Automaton' to set up the requirements, to specify and to execute small Computer Based Systems (CBS). A 'Parallel Automaton' is an extended form of the Mealy Machine. It handles a finite set of events (or variable conditions or clock conditions) which can occur in parallel, and performs a finite set of actions which can be done in paral...

A classical construction of Aho and Corasick solves the pattern matching problem for a finite set of words X in linear time, where the size of the input X is the sum of the lengths of its elements. It produces an automaton that recognizes A∗X, where A is a finite alphabet, but which is generally not minimal. As an alternative to classical minimization algorithms, which yields a O(n logn) soluti...

In [2], Blum and Hewitt introduced a two-dimensional finite automaton which can be considered as a natural extension of the one-dimensional two-way finite automaton [4] to two dimensions. On the other hand, in [7,8], Rosenfeld introduced a new type of automaton on a two-dimensional tape (called the three-way two-dimensional finite automaton) which can be considered as a natural extension of the...

This paper continues the study of the two-variable fragment of first-order logic (FO2) over twodimensional structures, more precisely structures with two orders, their induced successor relations and arbitrarily many unary relations. Our main focus is on ordered data words which are finite sequences from the set Σ×D where Σ is a finite alphabet and D is an ordered domain. These are naturally re...

The paper considers the generalized structure of maintenance system, including, in general case, protection subsystem, functional diagnostics test and repair subsystem. technical implementation listed subsystems is possible form tools built into object external to object. For transport technological machines ratios volumetric characteristics built-in are analyzed (using simplest analytical expr...

This paper explores the language classes that arise with respect to the head count of a finite ultrametric automaton. First we prove that in the one-way setting there is a language that can be recognized by a one-head ultrametric finite automaton and cannot be recognized by any k-head non-deterministic finite automaton. Then we prove that in the two-way setting the class of languages recognized...

In this paper, we propose a regular expression matching circuit based on a decomposed automaton. To implement a regular expression matching circuit, first, we convert regular expressions into a non-deterministic finite automaton (NFA). Then, to reduce the number of states, we convert the NFA into a modular non-deterministic finite automaton with unbounded string transition (MNFAU). Next, to rea...

Arden’s Lemma is a classical result in language theory allowing the computation of a rational expression denoting the language recognized by a finite string automaton. In this paper we generalize this important lemma to the rational tree languages. Moreover, we propose also a construction of a rational tree expression which denotes the accepted tree language of a finite tree automaton.