On Weighted Configuration Logics

Abstract

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...

Early validation of system requirements and design through correctness-by-construction

“…The set of styles in this article was derived by identifying commonalities in the base of natural language requirements of the case studies. Additional effort is required to this respect, whereas a recent research work opens prospects for defining styles which enforce quantitative properties [66].…”

Architectures in parametric component-based systems: Qualitative and quantitative modelling

“…(5) We introduce weighted Extended Propositional Interaction Logic (wEPIL for short) over a finite set of ports and a commutative semiring K for representing the weights. wEPIL extends weighted Propositional Interaction Logic (wPIL for short) from [PR17,PR20a] with three new weighted operators, namely the weighted concatenation operator , the weighted shuffle operator , and the weighted iteration operator ⊕ . Intuitively these operators allow to encode the weight of consecutive, interleaving, and recursive interactions in weighted component-based systems, respectively.…”

“…Finally, according to our best knowledge the only weighted logic-based approach for the modelling of architectures is found in the recent work of [KP20,PR17,PR20a]. Specifically, in [PR17,PR20a] the authors studied PCL in the weighted setup for modelling the quantitative aspects of architectures.…”

“…Finally, according to our best knowledge the only weighted logic-based approach for the modelling of architectures is found in the recent work of [KP20,PR17,PR20a]. Specifically, in [PR17,PR20a] the authors studied PCL in the weighted setup for modelling the quantitative aspects of architectures. The formulas of the resulting logic, namely weighted PCL (wPCL for short), were interpreted as polynomials with values over a commutative semiring.…”

Correct by construction model based design for systems and software

“…The set of styles was derived by identifying commonalities in the base of natural language requirements of the case studies. Additional effort is required to this respect, whereas a recent research work opens prospects for defining styles that enforce quantitative properties [80].…”