Two-Sided Derivatives for Regular Expressions and for Hairpin Expressions

Champarnaud, Jean-Marc; Dubernard, Jean-Philippe; Jeanne, Hadrien; Mignot, Ludovic

doi:10.1007/978-3-642-37064-9_19

Cited by 7 publications

(9 citation statements)

References 22 publications

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“…Given a regular language L, the (Myhill-Nerode) relation on Σ ⋆ , x L y if and only if (∀u)u ∈ Σ ⋆ , ux ∈ L ⇔ uy ∈ L is an equivalence relation with finite index and left invariant. The right quotient of L by a word u ∈ Σ ⋆ is the language Lu −1 = {x ∈ Σ ⋆ | xu ∈ L} and corresponds to an equivalence class of L , [CDJM13,Sak09]. For x, y ∈ Σ ⋆ , we define E L (x, y) = L −1 x∆L −1 y.…”

Section: Right Distinguishabilitymentioning

confidence: 99%

Distinguishability Operations and Closures

Câmpeanu

Moreira

Reis

2016

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Given a regular language L, we study the language of words D(L), that distinguish between pairs of different left-quotients of L. We characterize this distinguishability operation, show that its iteration has always a fixed point, and we generalize this result to operations derived from closure operators and Boolean operators. We give an upper bound for the state complexity of the distinguishability operation, and prove its tightness. We show that the set of minimal words that can be used to distinguish between different left-quotients of a language L has at most n − 1 elements, where n is the state complexity of L, and we also study the properties of its iteration. We generalize the results for the languages of words that distinguish between pairs of different right-quotients and two-sided quotients of a language L.

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Section: Right Distinguishabilitymentioning

confidence: 99%

Distinguishability Operations and Closures

Câmpeanu

Moreira

Reis

2016

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“…Moreover, it is easy to see that all pairs of states that contain the sink state are marked as pairs of distinguishable states, too. Then also the pairs (1, 2) and (1, 2 ′ ) are marked as pairs of distinguishable states: on taking a backward transition the pair (1, 2) goes to the previously marked pair (2 ′ , 3) and with a forward transition the pair (1, 2 ′ ) goes the marked pair to (2,3). Finally the remaining pair (2, 2 ′ ) is marked as pair of distinguishable states because on a forward transition state 2 goes to the sink state, while state 2 ′ goes to state 3.…”

Section: Proofmentioning

confidence: 99%

“…Simply speaking, a biautomaton is a device consisting of a deterministic finite control, a read-only input tape, and two reading heads, one reading the input from left to right, and the other head reading the input from right to left. Similar two-head finite automata models were introduced, e.g., in [3,8,11]. An input word is accepted by a biautomaton, if there is an accepting computation starting the heads on the two ends of the word meeting somewhere in an accepting state.…”

Section: Introductionmentioning

confidence: 99%

Minimization and Characterizations for Biautomata

Holzer

Jakobi

2015

Fundamenta Informaticae

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We show how to minimize biautomata with adaptations of classical minimization algorithms for ordinary deterministic finite automata and moreover by a Brzozowski-like minimization algorithm by applying reversal and power-set construction twice to the biautomaton under consideration. Biautomata were recently introduced in [O. KLÍMA, L. POLÁK: On biautomata. 46(4), 2012] as a generalization of ordinary finite automata, reading the input from both sides. The correctness of the Brzozowski-like minimization algorithm needs a little bit more argumentation than for ordinary finite automata since for a biautomaton its dual or reverse automaton, built by reversing all transitions, does not necessarily accept the reversal of the original language. To this end we first use the recently introduced notion of nondeterminism for biautomata [M. HOLZER, S. JAKOBI: Nondeterministic Biautomata and Their Descriptional Complexity. In: 15th DCFS, Number 8031 of LNCS, 2013] and take structural properties of the forward-and backward-transitions of the automaton into account. This results in a variety of biautomata models, the accepting power of which is characterized. As a byproduct we give a simple structural characterization of cyclic regular and commutative regular languages in terms of deterministic biautomata.

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“…A biautomaton consists of a deterministic finite control, a read-only input tape, and two reading heads, one reading the input from left to right, and the other head reading the input from right to left. Similar two-head finite automata models were introduced, e.g., in [3,13,16]. An input word is accepted by a biautomaton, if there is an accepting computation starting the heads on the two ends of the word meeting somewhere in an accepting state.…”

Section: Introductionmentioning

confidence: 99%

Nondeterministic Biautomata and Their Descriptional Complexity

Holzer

Jakobi

2014

Int. J. Found. Comput. Sci.

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We investigate the descriptional complexity of nondeterministic biautomata, which are a generalization of biautomata [O. Klíma, L. Polák: On biautomata. RAIRO -Theor. Inf. Appl., 46(4), 2012]. Simply speaking, biautomata are finite automata reading the input from both sides; although the head movement is nondeterministic, additional requirements enforce biautomata to work deterministically. First we study the size blow-up when determinizing nondeterministic biautomata. Further, we give tight bounds on the number of states for nondeterministic biautomata accepting regular languages relative to the size of ordinary finite automata, regular expressions, and syntactic monoids. It turns out that as in the case of ordinary finite automata nondeterministic biautomata are superior to biautomata with respect to their relative succinctness in representing regular languages.

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Two-Sided Derivatives for Regular Expressions and for Hairpin Expressions

Cited by 7 publications

References 22 publications

Distinguishability Operations and Closures

Distinguishability Operations and Closures

Minimization and Characterizations for Biautomata

Nondeterministic Biautomata and Their Descriptional Complexity

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