Multi-weighted Automata and MSO Logic

Droste, Manfred; Perevoshchikov, Vitaly

doi:10.1007/s00224-015-9658-9

Cited by 8 publications

(3 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Relations of various kinds of logics and automata are widely studied (see e.g. [32,29,16]), and our results provide new insights into this area for quantitative logics. Previous work [31] offered only translation of a similar logic to non-deterministic "mean-payoff Büchi automata" noting that it is difficult to give an analogous reduction to deterministic "mean-payoff Rabin automata".…”

Section: Introductionmentioning

confidence: 67%

Controller Synthesis for MDPs and Frequency LTL $$_{\setminus \mathbf{G}\mathbf U}$$

Forejt

Krăźál

Křetínský

2015

Logic for Programming, Artificial Intelligence, and Reasoning

View full text Add to dashboard Cite

Quantitative extensions of temporal logics have recently attracted significant attention. In this work, we study frequency LTL (fLTL), an extension of LTL which allows to speak about frequencies of events along an execution. Such an extension is particularly useful for probabilistic systems that often cannot fulfil strict qualitative guarantees on the behaviour. It has been recently shown that controller synthesis for Markov decision processes and fLTL is decidable when all the bounds on frequencies are 1. As a step towards a complete quantitative solution, we show that the problem is decidable for the fragment fLTL \GU , where U does not occur in the scope of G (but still F can). Our solution is based on a novel translation of such quantitative formulae into equivalent deterministic automata.

show abstract

Section: Introductionmentioning

confidence: 67%

Controller Synthesis for MDPs and Frequency LTL $$_{\setminus \mathbf{G}\mathbf U}$$

Forejt

Krăźál

Křetínský

2015

Logic for Programming, Artificial Intelligence, and Reasoning

View full text Add to dashboard Cite

show abstract

“…This work should be further extended to the multi-weighted setting for WTA, e.g., the optimal reward-cost ratio [7,8] or the optimal consumption of several resources where some resources must be restricted [22]. A logical characterization of untimed multi-weighted automata was given in [15]. It could be also interesting to compare for the weighted and unweighted cases the complexity of translations between logic and automata.…”

Section: Discussionmentioning

confidence: 99%

A Nivat Theorem for Weighted Timed Automata and Weighted Relative Distance Logic

Droste

Perevoshchikov

2014

Automata, Languages, and Programming

Self Cite

View full text Add to dashboard Cite

Abstract. Weighted timed automata (WTA) model quantitative aspects of real-time systems like continuous consumption of memory, power or financial resources. They accept quantitative timed languages where every timed word is mapped to a value, e.g., a real number. In this paper, we prove a Nivat theorem for WTA which states that recognizable quantitative timed languages are exactly those which can be obtained from recognizable boolean timed languages with the help of several simple operations. We also introduce a weighted extension of relative distance logic developed by Wilke, and we show that our weighted relative distance logic and WTA are equally expressive. The proof of this result can be derived from our Nivat theorem and Wilke's theorem for relative distance logic. Since the proof of our Nivat theorem is constructive, the translation process from logic to automata and vice versa is also constructive. This leads to decidability results for weighted relative distance logic.

show abstract

“…In fact, (R3) and (R4) seem to rule out some otherwise interesting quantities. However, there already exists a fully abstract model, which "maximizes" (R1) and (R2), but does not follow (R3) and (R4): multi-weighted automata of Droste and Perevoshchikov [11]. Practically any quantitative property can be realized in this model.…”

Section: Introductionmentioning

confidence: 99%

Automata with Auxiliary Weights

Kostolányi

Rovan

2016

Int. J. Found. Comput. Sci.

View full text Add to dashboard Cite

We introduce a new generalization of weighted automata – automata with auxiliary weights. They allow to compute several quantities not directly computable over semirings by generalizing both semiring addition and semiring multiplication. Moreover, our automata retain key properties of ordinary weighted automata. We prove that automata over multi-hemirings of Droste and Kuich [7] can be modelled using our framework, and that automata with auxiliary weights can be used to describe several additional settings. Finally, we introduce rational expressions with auxiliary weights and prove that they are equivalent to our automata.

show abstract

Multi-weighted Automata and MSO Logic

Cited by 8 publications

References 27 publications

Controller Synthesis for MDPs and Frequency LTL $$_{\setminus \mathbf{G}\mathbf U}$$

Controller Synthesis for MDPs and Frequency LTL $$_{\setminus \mathbf{G}\mathbf U}$$

A Nivat Theorem for Weighted Timed Automata and Weighted Relative Distance Logic

Automata with Auxiliary Weights

Contact Info

Product

Resources

About