ω-automaton

About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.

State Complexity of Nondeterministic Finite Automata with Limited Nondeterminism

Abstract: Various approaches of quantifying nondeterminism in nondeterministic finite automata (NFA) are considered. We consider nondeterministic finite automata having finite tree width (ftw-NFA) where the computation on any input string has a constant number of branches. We give effective characterizations of ftw-NFAs and a tight bound for determinizing an ftw-NFA A as a function of the tree width and the number of states of A. We introduce a lower bound technique for ftw-NFAs. We study the interrelationships between various measures of nondeterminism for finite automata. We define the trace measure which is a new approach of quantifying nondeterminism. The trace is defined in terms of the maximum product of the degrees of nondeterministic choices in any computation. We establish upper and lower bounds for the trace of an NFA in terms of its tree width. It is known that an NFA with n states and branching k can be simulated by a deterministic finite automaton with multiple initial states (MDFA) having k · n states. We give a lower bound k 1+log k · n for the size blow-up of this conversion. We also consider bounds for the number of states an MDFA needs to simulate a given NFA of finite tree width. i We consider unary NFA employing limited nondeterminism. We show that for unary regular languages, minimal ftw-NFAs can always be found in Chrobak normal form. A similar property holds with respect to other measures of nondeterminism. The latter observation is used to establish, for a given unary regular language, relationships between the sizes of minimal NFAs where the nondeterminism is limited in various ways. We study also the state complexity of language operations for unary NFAs with limited nondeterminism. We consider the operations of concatenation, Kleene star, and complement. We give upper bounds for the state complexity of these language operations and lower bounds that are fairly close to the upper bounds. Finally, we show that the branching measure (J. Goldstine, C. Kintala, D. Wotschke, Inf. and Comput vol 86, 1990, 179-194) of a unary NFA is always either bounded by a constant or has an exponential growth rate.

Finite Automata Implementations Considering CPU Cache

Abstract: The finite automata are mathematical models for finite state systems. More general finite automaton is the nondeterministic finite automaton (NFA) that cannot be directly used. It is usually transformed to the deterministic finite automaton (DFA) that then runs in time O(n), where n is the size of the input text. We present two main approaches to practical implementation of DFA considering CPU cache. The first approach (represented by Table Driven and Hard Coded implementations) is suitable forautomata being run very frequently, typically having cycles. The other approach is suitable for a collection of automata from which various automata are retrieved and then run. This second kind of automata are expected to be cycle-free.

A fast new semi-incremental algorithm for the construction of minimal acyclic DFAs

Abstract: We present a semi-incremental algorithm for constructing minimal acyclic deterministic finite automata. Such automata are useful for storing sets of words for spell-checking, among other applications. The algorithm is semi-incremental because it maintains the automaton in near-minimal condition and requires a final minimization step after the last word has been added (during construction). The algorithm derivation proceeds formally (with correctness arguments) from two separate algorithms, one for minimization and one for adding words to acyclic automata. The algorithms are derived in such a way as to be combinable, yielding a semi-incremental one. In practice, the algorithm is both easy to implement and displays good running time performance.

Minimal linear realizations of autonomous automata

Abstract: In the theory of finite automata minimal linear realizations of automata are of great interest. One can show that in the case of autonomous automata without output function it is sufficient to find minimal linear realizations of special types of automata, namely of permutations and of trees. Deriving this result we furthermore get the uniqueness of the minimal linear realization of a tree.

Formal partitioning analysis and verification of extended algebraic automata

Abstract: Algebraic automata is getting much importance in theoretical computer science because of its various applications, for example, in optimization of programs, verification of protocols, cryptography and modeling biological phenomena. Design of a complex system not only requires functionality but it also needs to capture its control behaviour. This paper is a part of our ongoing research on integration of algebraic automata and formal methods. Algebraic automaton is a powerful tool in modeling behaviour while Z is an ideal specification language used for describing statics of a system. Consequently, an integration of algebraic automata and Z will be a useful tool for modeling of complex systems. In this paper, we have described formal partitioning analysis of extended algebraic automata because of its use in components based modeling. At first, formal specification of constructing sub-automata for given automata is presented. Then equality of two given automata is verified. In next, cycles are identified and finally formal partitioning analysis of extended algebraic automata is provided. The formal specification is checked, analyzed and validated using Z/Eves tool. Key words: Algebraic automata, partitioning automata, component based modeling, Z notation, validation.