Generalising KAT to Verify Weighted Computations

Gomes, Leandro; Madeira, Alexandre; Barbosa, Lu­ís Soares

doi:10.7561/sacs.2019.2.141

Cited by 6 publications

(4 citation statements)

References 33 publications

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“…Indeed, it would be interesting to figure out a weighted generalization of other completeness proofs for Kleene algebra, such as [7]. An intriguing problem is also to extend our result to variants of Kleene algebra with tests where tests do not form a Boolean algebra [6].…”

Section: Discussionmentioning

confidence: 93%

“…Given the applications of Kleene algebra in reasoning about regular and while programs, it is natural to consider a Kleenealgebraic perspective on weighted programs. Gomes et al [6] formulate a generalization of KAT called graded KAT (or GKAT) where the Boolean algebra of tests is replaced by a more general algebraic structure. Batz et al [3] point out that a deeper study of the applicability of GKAT to reasoning about weighted programs is an interesting problem to look at.…”

Section: Kleene Algebra With Weights and Testsmentioning

confidence: 99%

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On the Complexity of Kleene Algebra with Domain

Sedlár

2023

Lecture Notes in Computer Science

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Weighted programs generalize probabilistic programs and offer a framework for specifying and encoding mathematical models by means of an algorithmic representation. Kleene algebra with tests is an algebraic formalism based on regular expressions with applications in proving program equivalence. We extend the language of Kleene algebra with tests so that it is sufficient to formalize reasoning about a simplified version weighted programs. We introduce relational semantics for the extended language, and we generalize the relational semantics to an appropriate extension of Kleene algebra with tests, called Kleene algebra with weights and tests. We demonstrate by means of an example that Kleene algebra with weights and tests offers a simple algebraic framework for reasoning about equivalence and optimal runs of weighted programs.

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Section: Discussionmentioning

confidence: 93%

Section: Kleene Algebra With Weights and Testsmentioning

confidence: 99%

On the Complexity of Kleene Algebra with Domain

Sedlár

2023

Lecture Notes in Computer Science

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“…We took, in this paper, the first step in order to develop a rigorous and systematic formalism for the verification of weighted concurrent systems, motivated by the fuzzy case. The approach is based on the combination of some ideas from previous research [15,18,8] to characterise both the computational and logical settings on top of which a proper (axiomatic, denotational and operational) semantics for fuzzy programs will be developed, in future work. There are numerous research lines that were left open and are worth to pursue in the near future.…”

Section: Resultsmentioning

confidence: 99%

On the Construction of Multi-valued Concurrent Dynamic Logics

Gomes

2020

Lecture Notes in Computer Science

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Dynamic logic is a powerful framework for reasoning about imperative programs. An extension with a concurrent operator [18] was introduced to formalise programs running in parallel. In other direction, other authors proposed a systematic method for generating multi-valued propositional dynamic logics to reason about weighted programs [14]. This paper presents the first step of combining these two frameworks to introduce uncertainty in concurrent computations. In the developed framework, a weight is assigned to each branch of the parellel execution, resulting in a (possible) asymmetric parallelism, inherent to fuzzy programming paradigm [21,2]. By adopting such an approach, a family of logics is obtained, called multi-valued concurrent propositional dynamic logics (CGDL(A)), parametric on an action lattice A specifying a notion of "weight" assigned to program execution. Additionally, the validity of some axioms of CPDL is discussed in the new family of generated logics. IntroductionOver time, the different variations of dynamic logics developed went hand-inhand with the very notion of its object, the program. This resulted in a diverse myriad of dynamic logics tailored to specific programming paradigms. Examples include probabilistic [11], concurrent [18], quantum [1] and continuous [19] computations, and combinations thereof. An example of another non-trivial paradigm is the fuzzy one [21,2], where the execution of a program differs from both classical and probabilistic scenarios: a conditional statement may act as a concurrent execution with a weight associated to each branch. The formalisation of such behaviour encompasses two non-trivial computational settings: concurrency and uncertainty. An extensive research can be found in the literature on diverse formalisms to reason about programs running in parallel [9,10] and to deal with uncertainty [11,5,20,4]. However, even when these two components are combined into a single framework [16], the uncertainty models probabilistic nondeterminism. Thus we are still missing a proper semantics to describe the behaviour of the fuzzy paradigm.Recently, reference [14] initiated a research agenda on the systematic development of multi-valued propositional dynamic logics, parametric on an action ⋆

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“…A more generic algebraic structure, suitable to deal with generic weighted computations was recently introduced by the authors in[7].…”

mentioning

confidence: 99%

Logics for Petri Nets with Propagating Failures

Gomes

Madeira

Benevides

2019

Fundamentals of Software Engineering

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Petri nets play a central role in the formal modelling of a wide range of complex systems and scenarios. Their ability to handle with both concurrency and resource awareness justifies their spread in the current formal development practices. On the logic side, Dynamic Logics are widely accepted as the de facto formalisms to reason about computational systems. However, as usual, the application to new situations raises new challenges and issues. The ubiquity of failures in the execution of current systems, interpreted in these models as triggered events that are not followed by the corresponding transition, entails not only the adjustment of these structures to deal with this reality, but also the introduction of new logics adequate to this emerging phenomenon. This paper contributes to this challenge by exploring a combination of two previous works of the authors, namely the Propositional Dynamic Logic for Petri Nets [1] and a parametric construction of multi-valued dynamic logics presented in [13]. This exercise results in a new family of Dynamic Logics for Petri Nets suitable to deal with firing failures.

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Generalising KAT to Verify Weighted Computations

Cited by 6 publications

References 33 publications

On the Complexity of Kleene Algebra with Domain

On the Complexity of Kleene Algebra with Domain

On the Construction of Multi-valued Concurrent Dynamic Logics

Logics for Petri Nets with Propagating Failures

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