Consider nondeterministic finite automata recognizing base-k positional notation of numbers. Assume that numbers are read starting from their least significant digits. It is proved that if two sets of numbers S and T are represented by nondeterministic automata of m and n states, respectively, then their sum {s+ t | s ∈ S, t ∈ T } is represented by a nondeterministic automaton with 2mn+2m+2n+1 ...

We describe an e cient CTL model checking algorithm based on alternating automata and games. A CTL formula, expressing a correctness property, is rst translated to a hesitant alternating automaton and then composed with a Kripke structure representing the model to be checked, this resulting automaton is then checked for nonemptiness. We introduce the nonemptiness game that checks the nonemptine...

We examine the conjecture that no polynomial can upper bound the increase in the number of states when a one-way nondeterministic finite automaton (1nfa) is converted into an equivalent two-way deterministic finite automaton (2dfa). We study the problem of liveness, which admits 1nfas of polynomial size and is known to defy 2dfas of polynomial size if and only if the conjecture is true. We focu...

Article history: Available online 2 February 2012 We present a novel technique, suitable for bit-parallelism, for representing both the nondeterministic automaton and the nondeterministic suffix automaton of a given string in a more compact way. Our approach is based on a particular factorization of strings which on the average allows to pack in a machine word of w bits automata state configura...

Several optimal algorithms have been proposed for the complementation of nondeterministic Büchi word automata. Due to the intricacy of the problem and the exponential blow-up that complementation involves, these algorithms have never been used in practice, even though an effective complementation construction would be of significant practical value. Recently, Kupferman and Vardi described a com...

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 the transition weights. When the mode of branching of the automaton is deterministic, nondeterministic, or alternating, the corresponding class of quantitative...

We follow a connection between tight determinisation and complementation and establish a complementation procedure from transition-labelled parity automata to transition-labelled nondeterministic Büchi automata. We prove it to be tight up to an O(n) factor, where n is the size of the nondeterministic parity automaton. This factor does not depend on the number of priorities.

Finite (nondeterministic) automata are very useful building blocks in the field of string matching. This is particularly true in the case of multiple pattern matching, where the use of factor-based automata can reduce substantially the number of computational steps when the patterns have large common factors. Direct simulation of nondeterministic automata can be performed very efficiently using...

In this paper, we propose a novel algorithm to learn Büchi automaton from teacher who knows an ? -regular language. The learned can be nondeterministic or limit deterministic automaton. learning is based on formalism called family of DFAs (FDFAs) recently proposed by Angluin and Fisman. main catch that use classification tree structure instead the standard observation table structure. worst cas...

In an earlier paper, the author used derivatives to construct a deterministic automaton recognizing the language defined by an ω-regular expression. The construction was related to a determinization method invented by Safra. This paper describes a new construction, inspired by Piterman’s improvement to Safra’s method. It produces an automaton with fewer states. In addition, the presentation and...