In this paper we study a large number of logics to define languages of unordered unranked trees and compare their expressive power. Generally speaking, the logics we consider stem from three non-disjoint areas: logics related to automata theory, logics discussed in descriptive complexity theory, and second-order logics. The basic logic from automata theory is monadic second-order logic. Two ext...

The paper shows how some semigroup-theory methods can be used in automata problems. The theory of automata is closely connected with the theory of semigroups (or, to be more exact, with the theory of representations of semigroups by transformations). The concept of automaton without outputs is equivalent to the concept of representa­ tion of free semigroup by transformations. If we consider eve...

Parity word automata and their determinisation play an important role in automata and game theory. We discuss a determinisation procedure for nondeterministic parity automata through deterministic Rabin to deterministic parity automata. We prove that the intermediate determinisation to Rabin automata is optimal. We show that the resulting determinisation to parity automata is optimal up to a sm...

In classical Formal Language Theory, “centralised” grammar systems and automata were the standard models for computation devices. With the rapid growth of computer networks, distributed databases, etc, distributed computation has begun to play a major role in modern computer science. The theory of grammar systems and distributed-automata was thus developed as a model for distributed computation...

Supervisory control of the mobile robot navigation system has critical importance. The supervisory control software development of mobile robot navigation can be performed in an unknown environment or for controlled robots in a known environment. Finite automata and graph theory are functional tools in modeling the robot navigation system through discrete environment. This research has emphasis...

The aim of this thesis is to provide verification techniques based on formal language theory and graph theory for graph transformation systems. Graph transformation systems can be used in a large number of application areas. In many cases it is very natural to model concurrent and distributed systems or other systems, where evolving graph-like structures play a role, by means of graph transform...

Interrupt Timed Automata (ITA ) form a subclass of stopwatch automata where reachability and some variants timed model checking are decidable even in presence parameters. They well suited to analyze real-time operating systems. Here we extend ITA with polynomial guards updates, leading the class (PolITA ). We prove that is 2EXPTIME on PolITA, using an adaptation cylindrical algebraic decomposit...

In this paper, a mathematical schema theory is developed. This theory has three roots: brain theory schemas, grid automata, and block-shemas. In Section 2 of this paper, elements of the theory of grid automata necessary for the mathematical schema theory are presented. In Section 3, elements of brain theory necessary for the mathematical schema theory are presented. In Section 4, other types of...

The languages accepted by finite automata are precisely the languages denoted by regular expressions. In contrast, finite automata may exhibit behaviours that cannot be described by regular expressions up to bisimilarity. In this paper, we consider extensions of the theory of regular expressions with various forms of parallel composition and study the effect on expressiveness. First we prove th...

In this thesis we investigate decidable and computational properties of Cellular Automata. This investigation is intended to be a contribute to the study of the more general theory of Complex Systems. A central interest in the sciences of complex systems is to understand the laws by which a global complex behavior can emerge for the collective interaction of simple components. Computation Theor...