The state complexity of random DFAs

Autor: Aryeh Kontorovich, Daniel Berend
Rok vydání: 2016
Předmět:
FOS: Computer and information sciences
General Computer Science
Formal Languages and Automata Theory (cs.FL)
Computer Science - Formal Languages and Automata Theory
0102 computer and information sciences
02 engineering and technology
01 natural sciences
60C05
68Q45
Theoretical Computer Science
Set (abstract data type)
FOS: Mathematics
0202 electrical engineering
electronic engineering
information engineering
Mathematics - Combinatorics
Computer Science::Data Structures and Algorithms
Mathematics
Discrete mathematics
High probability
Probability (math.PR)
Automaton
State complexity
010201 computation theory & mathematics
020201 artificial intelligence & image processing
Combinatorics (math.CO)
Alphabet
Constant (mathematics)
Mathematics - Probability
Computer Science::Formal Languages and Automata Theory
Zdroj: Theoretical Computer Science. 652:102-108
ISSN: 0304-3975
Popis: The state complexity of a Deterministic Finite-state automaton (DFA) is the number of states in its minimal equivalent DFA. We study the state complexity of random $n$-state DFAs over a $k$-symbol alphabet, drawn uniformly from the set $[n]^{[n]\times[k]}\times2^{[n]}$ of all such automata. We show that, with high probability, the latter is $\alpha_k n + O(\sqrt n\log n)$ for a certain explicit constant $\alpha_k$.
Databáze: OpenAIRE
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