We describe a new method of synthesizing a formal model for real-time systems from scenarios. Scenarios, formally defined as Timed Event Sequences, together with mode graphs are used to describe behaviors of real-time systems. Given a set of Timed Event Sequences and a mode graph, our synthesis method constructs a minimal, acyclic, deterministic timed automaton that models the specified aspects...

In this paperwe adapt thewell-knownBrzozowskideterminizationmethod to fuzzy automata. Thismethod gives better results than all previously knownmethods for determinization of fuzzy automata developed by Bělohlávek [InformSciences 143 (2002)205–209],Li andPedrycz [FuzzySet Syst 156 (2005)68–92], Ignjatović et al. [Inform Sciences 178 (2008) 164–180], and Jančić et al. [Inform Sciences 181 (2011) ...

GP (for Graph Programs) is a rule-based, nondeterministic programming language for solving graph problems at a high level of abstraction, freeing programmers from dealing with low-level data structures. In this case study, we present a graph program which minimizes finite automata. The program represents an automaton by its transition diagram, computes the state equivalence relation, and merges...

This paper introduces and formalizes a new variant of Timed Automata, called Time Labeled Scheduling Automata. A Time Labeled Scheduling Automaton is a single clock implementation model expressing globally the time constraints that a system has to meet. An algorithm is presented to show how a Time Labeled Scheduling Automaton can be synthesized from a minimal reachability graph derived from a h...

The work presents some new algorithms realized recently in the package TESTAS. The package decides whether or not DFA is synchronizing, several procedures find relatively short synchronizing words and a synchronizing word of the minimal length. We check whether or not a directed graph has a road coloring that turns the graph into a synchronizing deterministic finite automaton (DFA). The algorit...

AUTOMATE is a package for symbolic computation on nite automata, extended rational expressions and nite semigroups. On the one hand, it enables one to compute the deterministic minimal automaton of the language represented by a rational expression or given by its table. On the other hand, given the transition table of a deterministic automaton, AUTOMATE computes the associated transition monoid...

Previously, self-verifying symmetric difference automata were defined and a tight bound of 2n−1−1 was shown for state complexity in the unary case. We now consider the non-unary case and show that, for every n≥ 2, there is a regular languageLn accepted by a non-unary self-verifying symmetric difference nondeterministic automaton with n states, such that its equivalent minimal deterministic fini...

A word w is called synchronizing (recurrent, reset, directed) word of a deterministic finite automaton (DFA) if w sends all states of the automaton on a unique state. Jan Černy had found in 1964 a sequence of n-state complete DFA with shortest synchronizing word of length (n− 1). He had conjectured that it is an upper bound for the length of the shortest synchronizing word for any n-state compl...

Alternating automata on infinite trees induce operations on languages which do not preserve natural equivalence relations, like having the same Mostowski–Rabin index, the same Borel rank, or being continuously reducible to each other (Wadge equivalence). In order to prevent this, alternation needs to be restricted to the choice of direction in the tree. For weak alternating automata with restri...

A word w is called synchronizing (recurrent, reset, directable) word of deterministic finite automaton (DFA) if w brings all states of the automaton to an unique state. Černy conjectured in 1964 that every nstate synchronizable automaton possesses a synchronizing word of length at most (n− 1). The problem is still open. It will be proved that the minimal length of synchronizing word is not grea...