Glushkov construction
E632952
Glushkov construction is a method in automata theory that converts a regular expression into an equivalent nondeterministic finite automaton with a specific position-based structure.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
automata theory construction method
ⓘ
formal language theory concept ⓘ |
| alsoKnownAs |
position automata method
ⓘ
position automaton construction ⓘ position-based NFA construction NERFINISHED ⓘ |
| application |
conversion of regular expressions to automata in compilers
ⓘ
implementation of regular expression matchers ⓘ theoretical analysis of regular languages ⓘ |
| assumes | regular expression over a finite alphabet ⓘ |
| category | construction of automata from regular expressions ⓘ |
| comparedTo |
Thompson construction uses ε-transitions while Glushkov construction does not
ⓘ
position automaton is often more compact than Thompson NFA for the same regular expression ⓘ |
| complexity | polynomial-time in the size of the regular expression ⓘ |
| defines |
a state for each occurrence of an alphabet symbol in the regular expression
ⓘ
accepting states based on last positions of the regular expression ⓘ transitions based on the follow-position relation ⓘ |
| field |
automata theory
ⓘ
formal language theory ⓘ |
| formalizes | a direct correspondence between regex symbol positions and NFA states ⓘ |
| goal | convert a regular expression into an equivalent NFA ⓘ |
| guarantees | language equivalence between the regular expression and the constructed NFA ⓘ |
| historicalContext | introduced in the 1960s ⓘ |
| influenced | later work on position-based automata ⓘ |
| inputType | regular expression ⓘ |
| isPartOf | the theory of regular languages ⓘ |
| namedAfter | Victor M. Glushkov NERFINISHED ⓘ |
| outputType |
nondeterministic finite automaton
ⓘ
ε-free NFA ⓘ |
| producesAutomatonWith |
a unique initial state
ⓘ
no ε-transitions ⓘ states corresponding to positions of symbols in the regular expression ⓘ transition structure derived from symbol positions ⓘ |
| property |
avoids ε-transitions by design
ⓘ
constructs an automaton whose number of states equals the number of symbol occurrences plus one ⓘ structurally reflects the syntax of the regular expression ⓘ |
| relatedTo |
Brzozowski derivative construction
NERFINISHED
ⓘ
McNaughton–Yamada construction NERFINISHED ⓘ Thompson construction NERFINISHED ⓘ finite automaton minimization ⓘ position automaton ⓘ |
| typicalOutputAutomaton | position automaton of the given regular expression ⓘ |
| usedIn |
design of pattern matching algorithms
ⓘ
formal verification of systems specified by regular expressions ⓘ symbolic model checking of regular properties ⓘ |
| usesConcept |
first-position set of a regular expression
ⓘ
follow-position relation ⓘ last-position set of a regular expression ⓘ position of symbol in regular expression ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.