In the theory of computation and automata theory, the powerset construction or subset construction is a standard method for converting a nondeterministic finite automaton (NFA) into a deterministic finite automaton (DFA) which recognizes the same formal language. It is important in theory because it establishes that NFAs, despite their additional flexibility, are unable to recognize any language that cannot be recognized by some DFA. It is also important in practice for converting easier-to-construct NFAs into more efficiently executable DFAs. However, if the NFA has n states, the resulting DFA may have up to 2n states, an exponentially larger number, which sometimes makes the construction impractical for large NFAs.
The construction, sometimes called the Rabin–Scott powerset construction (or subset construction) to distinguish it from similar constructions for other types of automata, was first published by Michael O. Rabin and Dana Scott in 1959.[1]
^Rabin, M. O.; Scott, D. (1959). "Finite automata and their decision problems". IBM Journal of Research and Development. 3 (2): 114–125. doi:10.1147/rd.32.0114. ISSN 0018-8646.
and 18 Related for: Powerset construction information
In the theory of computation and automata theory, the powersetconstruction or subset construction is a standard method for converting a nondeterministic...
several arrows of the same label starting from a state. Using the powersetconstruction method, every NFA can be translated to a DFA that recognizes the...
the powersetconstruction, which may lead to an exponential rise in the number of necessary states. For a formal proof of the powersetconstruction, please...
⇒ 2. by Thompson's construction algorithm 2. ⇒ 1. by Kleene's algorithm or using Arden's lemma 2. ⇒ 3. by the powersetconstruction 3. ⇒ 2. since the former...
finite automaton from a nondeterministic finite automaton is the powersetconstruction.: 44 Anderson, James A. (2006). Automata theory with modern applications...
simultaneously traces all the possible execution paths of N (see powersetconstruction for this technique in use for finite automata). Another is randomization...
original language. Converting this NFA to a DFA using the standard powersetconstruction (keeping only the reachable states of the converted DFA) leads to...
n {\displaystyle 2^{n}} states by performing a similar kind of powersetconstruction as used for the transformation of an NFA to a DFA. The membership...
length at most 1. NFAs, in turn, can be reduced to DFAs using the powersetconstruction. This shows that GNFAs recognize the same set of formal languages...
minimizing the number of states in a deterministic finite automaton Powersetconstruction: algorithm to convert nondeterministic automaton to deterministic...
semantics Scott–Potter set theory Scott–Strachey semantics Rabin–Scott powersetconstruction Awards Leroy P. Steele Prize (1972) Turing Award (1976) Tarski Lectures...
by John G.F. Francis and Vera Kublanovskaya 1959 – Rabin–Scott powersetconstruction for converting NFA into DFA published by Michael O. Rabin and Dana...
preferable in this case. TNFA determinization is based on the canonical powersetconstruction algorithm that converts an NFA to a DFA. The algorithm simulates...
non-determinism. Just as the finite-powersetconstruction is the free semilattice, the powerdomain constructions should be understood abstractly as free...
cardinal λ is a strong limit cardinal if λ cannot be reached by repeated powerset operations. This means that λ is nonzero and, for all κ < λ, 2κ < λ. Every...
original on 5 April 2008. Retrieved 14 January 2022. "Tulsi Lake - Powerset". www.powerset.com. Archived from the original on 7 December 2008. Retrieved 14...
search results: examples include Microsoft Bing (via technology gained from Powerset) and DuckDuckGo. Collections of Wikipedia articles have been published...
Lankapuvath. 12 November 2018. Retrieved 27 November 2022. "New train engine and powerset lands in Sri Lanka". News First. 3 December 2018. Retrieved 27 November...
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