Abstract
We approach the problem of computing a D2-synchronizing word of minimum length for a given nondeterministic automaton via its encoding as an instance of SAT and invoking a SAT solver. In addition, we report some of the experimental results obtained when we had tested our method on randomly generated automata and certain benchmarks.
Highlights
A nondeterministic finite automaton (NFA) is a triple A = (Q, Σ, δ), where Q is a finite nonempty set of states, Σ is a finite non-empty set of input symbols, and δ is a map Q × Σ → P(Q), where P(Q) is the power set of Q
For random NFAs generated under the Poisson model, our experiments show that if the parameter λ is fixed, the length of the shortest proper D2-synchronizing word grows with the number of states but the growth rate is rather small
We have presented a modification of the approach originated in [12] that has allowed us to find shortest proper D2-synchronizing words for nondeterministic automata with two input letters and up to 100 states
Summary
A nondeterministic finite automaton (NFA) is a triple A = (Q, Σ, δ), where Q is a finite nonempty set of states, Σ is a finite non-empty set of input symbols, and δ is a map Q × Σ → P(Q), where P(Q) is the power set of Q. The map δ is called the transition function of A ; it describes the action of symbols in Σ at states in Q. The set of all words over Σ including the empty word is denoted by Σ∗. Al ∈ Σ is a non-empty word over Σ, the number l is said to be the length of w and is denoted by |w|. The set of all words of a given length l over Σ is denoted by Σl
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