Operations on Boolean and Alternating Finite Automata

Hospodár, Michal; Jirásková, Galina; Krajňáková, Ivana

doi:10.1007/978-3-319-90530-3_16

Cited by 4 publications

(4 citation statements)

References 15 publications

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“…If L is accepted by an n-state BFA, then L R is accepted by a 2 n -state DFA by Corollary 3. Then (L R ) * is accepted by a 2 2 n -state DFA with half of its state final [6,Proposition 8]. Next, we have (L * ) R = (L R ) * .…”

Section: Operational Complexity On Boolean and Alternating Finite Aut...mentioning

confidence: 99%

“…Boolean and alternating finite automata [1,2,6,7,10,11,12] are generalizations of nondeterministic finite automata. They recognize regular languages, however, they may be exponentially smaller, with respect to the number of states, than equivalent nondeterministic finite automata (NFAs).…”

Section: Introductionmentioning

confidence: 99%

“…Here we present the results obtained in [5,6,7,8,11] that provide the exact complexity of basic regular operations on languages represented by Boolean and alternating finite automata. Table 1 summarizes these results.…”

Section: Introductionmentioning

confidence: 99%

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Operations on Boolean and Alternating Finite Automata

Jirásková

2023

Electron. Proc. Theor. Comput. Sci.

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We examine the complexity of basic regular operations on languages represented by Boolean and alternating finite automata. We get tight upper bounds m + n and m + n + 1 for union, intersection, and difference, 2 m + n and 2 m + n + 1 for concatenation, 2 n + n and 2 n + n + 1 for square, m and m + 1 for left quotient, 2 m and 2 m + 1 for right quotient. We also show that in both models, the complexity of complementation and symmetric difference is n and m + n, respectively, while the complexity of star and reversal is 2 n . All our witnesses are described over a unary or binary alphabets, and whenever we use a binary alphabet, it is always optimal.

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Section: Operational Complexity On Boolean and Alternating Finite Aut...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Operations on Boolean and Alternating Finite Automata

Jirásková

2023

Electron. Proc. Theor. Comput. Sci.

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“…The emptiness problem for AFAs was shown to be PSPACE-Complete for general alphabets [8,12]. More recently, the state complexity of various operations on AFAs has also been studied [9].…”

Section: Introductionmentioning

confidence: 99%

Alternating Finite Automata with Limited Universal Branching

Keeler

Salomaa

2020

Language and Automata Theory and Applications

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We consider measures that limit universal parallelism in computations of an alternating finite automaton (AFA). Maximum pared tree width counts the largest number of universal branches in any computation and acceptance width counts the number of universal branches in the best accepting computation, i.e., in the accepting computation with least universal parallelism. We give algorithms to decide whether the maximum pared tree width or the acceptance width of an AFA are bounded by an integer k. For a constant k the algorithm for maximum pared tree width operates in polynomial time. An AFA with m states and acceptance width k can be converted to an NFA with (m + 1) k states. We consider corresponding lower bounds for the transformation. The tree width of an AFA counts the number of all (existential and universal) branches of the computation. We give upper and lower bounds for converting an AFA of bounded tree width to a DFA.

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Combining Limited Parallelism and Nondeterminism in Alternating Finite Automata

Keeler

Salomaa

2020

Lecture Notes in Computer Science

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Operations on Boolean and Alternating Finite Automata

Cited by 4 publications

References 15 publications

Operations on Boolean and Alternating Finite Automata

Operations on Boolean and Alternating Finite Automata

Alternating Finite Automata with Limited Universal Branching

Combining Limited Parallelism and Nondeterminism in Alternating Finite Automata

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