Weighted Linear Dynamic Logic

Droste, Manfred; Rahonis, George

doi:10.4204/eptcs.226.11

Cited by 2 publications

(4 citation statements)

References 31 publications

(67 reference statements)

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Section: Introductionmentioning

confidence: 99%

“…[1]), the weighted FO logic [8,9,10], the weighted LTL (cf. for instance [3] and the references in that paper), the weighted LDL [3], as well as the weighted MSO logic and LDL over infinite alphabets [12], and the weighted µ-calculus and CTL [7].The main contributions of our work are the following. We prove that for every weighted PCL formula we can effectively construct an equivalent one in full normal form which is unique up to the equivalence relation.…”

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confidence: 99%

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On Weighted Configuration Logics

Paraponiari

Rahonis

2017

Formal Aspects of Component Software

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We introduce and investigate a weighted propositional configuration logic over a commutative semiring. Our logic, which is proved to be sound and complete, is intended to serve as a specification language for software architectures with quantitative features. We extend the weighted configuration logic to its first-order level and succeed in describing architecture styles equipped with quantitative characteristics. We provide interesting examples of weighted architecture styles. Surprisingly, we can construct a formula, in our logic, which describes a classical problem of a different nature than that of software architectures.costs of the interactions among the components of an architecture, the time needed, the probability of the implementation of a concrete interaction, etc. Our weighted PCL consists of the PCL of [11] which is interpreted in the same way, and a copy of it which is interpreted quantitatively. This formulation has the advantage that practitioners can use the PCL exactly as they are used to, and the copy of it for the quantitative interpretation. The semantics of weighted PCL formulas are polynomials with values in the semiring K. The semantics of the unweighted PCL formulas take only the values 1 and 0 corresponding to true and f alse, respectively. Weighted logics have been considered so far in other set-ups. More precisely, the weighted MSO logic over words, trees, pictures, nested words, timed words, and graphs (cf. [1]), the weighted FO logic [8,9,10], the weighted LTL (cf. for instance [3] and the references in that paper), the weighted LDL [3], as well as the weighted MSO logic and LDL over infinite alphabets [12], and the weighted µ-calculus and CTL [7].The main contributions of our work are the following. We prove that for every weighted PCL formula we can effectively construct an equivalent one in full normal form which is unique up to the equivalence relation. Furthermore, our weighted PCL is sound and complete. Both the aforementioned results hold also for PCL and this shows the robustness of the theory of PCL. We prove several properties for the weighted first-order configuration logic and in addition for its Boolean counterpart of [11]. We present as an example the weighted PCL formula describing the Master/Slave architecture with quantitative features. According to the underlying semiring, we get information for the cost, probability, time, etc. of the implementation of an interaction between a Master and a Slave. We construct a weighted firstorder configuration logic formula for the Publish/Subscribe architecture style with additional quantitative characteristics. Surprisingly, though PCL was mainly developed as a specification language for architectures, we could construct a weighted PCL formula describing the wellknown travelling salesman problem.The structure of our paper is as follows. Apart from this Introduction the paper contains 5 sections. In Section 2 we present preliminary background needed in the sequel. In Section 3 we introduce the weighted proposition interaction log...

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

On Weighted Configuration Logics

Paraponiari

Rahonis

2017

Formal Aspects of Component Software

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“…In [20] the authors proved the coincidence of the classes of rational and LDL-definable languages interpreted over finite words. Recently, LDL has been investigated in the quantitative setup for both finite and infinite words [16]. More precisely, the authors proved the expressive equivalence of weighted LDL formulas to weighted automata for finite words over commutative semirings, and for infinite words over totally commutative complete semirings.…”

Section: Weighted Linear Dynamic Logic Over Infinite Alphabetsmentioning

confidence: 99%

“…In this section, we introduce a weighted LDL over the infinite alphabet Σ and the commutative semiring K, and we show the expressive equivalence of weighted LDL formulas to weighted variable automata. Let us firstly recall the basic definitions for weighted LDL logic over finite alphabets [16]. Let ∆ be a finite alphabet.…”

Section: Weighted Linear Dynamic Logic Over Infinite Alphabetsmentioning

confidence: 99%

Weighted Recognizability over Infinite Alphabets

Pittou¹,

Rahonis²

2017

Acta Cybern

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We introduce weighted variable automata over infinite alphabets and commutative semirings. We prove that the class of their behaviors is closed under sum, and under scalar, Hadamard, Cauchy, and shuffle products, as well as star operation. Furthermore, we consider rational series over infinite alphabets and we state a Kleene-Schützenberger theorem. We introduce a weighted monadic second order logic and a weighted linear dynamic logic over infinite alphabets and investigate their relation to weighted variable automata. An application of our theory, to series over the Boolean semiring, concludes to new results for the class of languages accepted by variable automata.

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Weighted Linear Dynamic Logic

Cited by 2 publications

References 31 publications

On Weighted Configuration Logics

On Weighted Configuration Logics

Weighted Recognizability over Infinite Alphabets

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