Parity automaton

Parity automaton

A parity automaton is a variant of a finite state automaton that accepts infinite inputs. Unlike usual finite state automata, there is no set of final states; instead, each state is assigned a natural number. It accepts an infinite input sequence if and only if there exists a run of the automaton (in case of a deterministic automaton, there is exactly one possible run) that satisfies the "parity condition": the largest number occurring infinitely often is even. It is equivalent to require that the least number occurring infinitely often be even.

Parity automata are generalizations of Büchi automata. Streett, Rabin, and Muller automata are generalizations of parity automata.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

  • ω-automaton — In automata theory, a branch of theoretical computer science, an ω automaton (or stream automaton) is a deterministic or nondeterministic automaton that runs on infinite, rather than finite, strings as input. Since ω automata do not stop, they… …   Wikipedia

  • Muller automaton — In automata theory, a Muller automaton is a type of an ω automaton. The acceptance condition separates a Muller automomaton from other ω automata. The Muller automata is defined using Muller acceptance condition, i.e. the set of all states… …   Wikipedia

  • Büchi automaton — A Büchi automaton is the extension of a finite state automaton to infinite inputs. It accepts an infinite input sequence iff there exists a run of the automaton (in case of a deterministic automaton, there is exactly one possible run) which… …   Wikipedia

  • Block cellular automaton — The Margolus neighborhood for a two dimensional block cellular automaton. The partition of the cells alternates between the set of 2 × 2 blocks indicated by the solid blue lines, and the set of blocks indicated by the dashed red lines. A block… …   Wikipedia

  • Rule 184 — is a one dimensional binary cellular automaton rule, notable for solving the majority problem as well as for its ability to simultaneously describe several, seemingly quite different, particle systems:* Rule 184 can be used as a simple model for… …   Wikipedia

  • Regular language — In theoretical computer science, a regular language is a formal language (i.e., a possibly infinite set of finite sequences of symbols from a finite alphabet) that satisfies the following equivalent properties: * it can be accepted by a… …   Wikipedia

  • List of mathematics articles (P) — NOTOC P P = NP problem P adic analysis P adic number P adic order P compact group P group P² irreducible P Laplacian P matrix P rep P value P vector P y method Pacific Journal of Mathematics Package merge algorithm Packed storage matrix Packing… …   Wikipedia

  • Pascal's triangle — The first six rows of Pascal s triangle In mathematics, Pascal s triangle is a triangular array of the binomial coefficients in a triangle. It is named after the French mathematician, Blaise Pascal. It is known as Pascal s triangle in much of the …   Wikipedia

  • List of algorithms — The following is a list of the algorithms described in Wikipedia. See also the list of data structures, list of algorithm general topics and list of terms relating to algorithms and data structures.If you intend to describe a new algorithm,… …   Wikipedia

  • Chaos theory — This article is about chaos theory in Mathematics. For other uses of Chaos theory, see Chaos Theory (disambiguation). For other uses of Chaos, see Chaos (disambiguation). A plot of the Lorenz attractor for values r = 28, σ = 10, b = 8/3 …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”