Incomplete Transition Complexity of Some Basic Operations

Maia, Eva; Moreira, Nelma; Reis, Rui L.

doi:10.1007/978-3-642-35843-2_28

Cited by 6 publications

(10 citation statements)

References 15 publications

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“…Note that the values in the table are obtained using languages for which the upper bounds are reached. This paper expands the work presented in extended abstracts [16,15] with full proofs of theorems and experimental tests.…”

Section: Introductionmentioning

confidence: 71%

Incomplete operational transition complexity of regular languages

Maia

Moreira

Reis

2015

Information and Computation

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The state complexity of basic operations on regular languages considering complete deterministic finite automata (DFA) has been extensively studied in the literature. But, if incomplete DFAs are considered, transition complexity is also an significant measure. In this paper we study the incomplete (deterministic) state and transition complexity of some operations for regular and finite languages. For regular languages we give a new tight upper bound for the transition complexity of the union, which refutes the conjecture presented by Y. Gao et al.. For finite languages, we correct the published state complexity of concatenation for complete DFAs and provide a tight upper bound for the case when the right operand is larger than the left one. We also present some experimental results to test the behaviour of those operations on the average case, and we conjecture that for many operations and in practical applications the worst-case complexity is seldom reached.

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Section: Introductionmentioning

confidence: 71%

Incomplete operational transition complexity of regular languages

Maia

Moreira

Reis

2015

Information and Computation

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“…In this section, we review the complexity of the algorithms presented in the previous section for the construction of DFAs from TWTL formulae. The complexity of basic composition operations for incomplete and acyclic DFAs has been explored in [25,14,6,11,8]. Our construction algorithms differ from the ones in the literature because we specialized and optimized them to translate TWTL formulae and handle words over power sets of atomic propositions.…”

Section: E Complexitymentioning

confidence: 99%

“…We also present an automata-based framework for minimizing the temporal relaxation of a given TWTL formula in problems related to verification, synthesis, and learning. In the theoretical computer science literature, finite languages and the complexity of construction their corresponding automata have been extensively studied [25,14,6,11,8]. The algorithms proposed in this paper are specialized to handle TWTL formulae and produce the annotated automata, which is used to solve synthesis, verification and learning problems efficiently.…”

Section: Introductionmentioning

confidence: 99%

Time window temporal logic

Vasile

Aksaray

Belta

2017

Theoretical Computer Science

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Abstract-This paper introduces time window temporal logic (TWTL), a rich expressivity language for describing various time bounded specifications. In particular, the syntax and semantics of TWTL enable the compact representation of serial tasks, which are typically seen in robotics and control applications. This paper also discusses the relaxation of TWTL formulae with respect to deadlines of tasks. Efficient automata-based frameworks to solve synthesis, verification and learning problems are also presented. The key ingredient to the presented solution is an algorithm to translate a TWTL formula to an annotated finite state automaton that encodes all possible temporal relaxations of the specification. Case studies illustrating the expressivity of the logic and the proposed algorithms are included.

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“…This motivates the study of the transition complexity of DFAs (not necessarily complete), besides the usual state complexity. The operational transition complexity of basic operations on regular languages was studied by Gao et al [5] and Maia et al [8]. In this paper we continue that line of research by considering the class of finite languages.…”

Section: Introductionmentioning

confidence: 67%

“…Given an incomplete DFA A = ([0, m − 1], Σ, δ A , 0, F A ) accepting a finite language, a DFA B accepting L(A) ⋆ can be constructed by an algorithm similar to the one for regular languages [8]. Let B = (Q B , Σ, δ B , {0}, F B ) where…”

Section: Starmentioning

confidence: 99%

Incomplete Transition Complexity of Basic Operations on Finite Languages

Maia

Moreira

Reis

2013

Implementation and Application of Automata

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Abstract. The state complexity of basic operations on finite languages (considering complete DFAs) has been in studied the literature. In this paper we study the incomplete (deterministic) state and transition complexity on finite languages of boolean operations, concatenation, star, and reversal. For all operations we give tight upper bounds for both descriptional measures. We correct the published state complexity of concatenation for complete DFAs and provide a tight upper bound for the case when the right automaton is larger than the left one. For all binary operations the tightness is proved using family languages with a variable alphabet size. In general the operational complexities depend not only on the complexities of the operands but also on other refined measures.

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Incomplete Transition Complexity of Some Basic Operations

Cited by 6 publications

References 15 publications

Incomplete operational transition complexity of regular languages

Incomplete operational transition complexity of regular languages

Time window temporal logic

Incomplete Transition Complexity of Basic Operations on Finite Languages

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