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Deciding Synchronous Kleene Algebra with Derivatives

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Book cover Implementation and Application of Automata (CIAA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9223))

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Abstract

Synchronous Kleene algebra (SKA) is a decidable framework that combines Kleene algebra (KA) with a synchrony model of concurrency. Elements of SKA can be seen as processes taking place within a fixed discrete time frame and that, at each time step, may execute one or more basic actions or then come to a halt. The synchronous Kleene algebra with tests (SKAT) combines SKA with a Boolean algebra. Both algebras were introduced by Prisacariu, who proved the decidability of the equational theory, through a Kleene theorem based on the classical Thompson \(\varepsilon \)-NFA construction. Using the notion of partial derivatives, we present a new decision procedure for equivalence between SKA terms. The results are extended for SKAT considering automata with transitions labeled by Boolean expressions instead of atoms. This work continous previous research done for KA and KAT, where derivative based methods were used in feasible algorithms for testing terms equivalence.

This work was partially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020, and through the programme COMPETE and by the Portuguese Government through the FCT under project FCOMP-01-0124-FEDER-020486.

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Notes

  1. 1.

    Source code at http://www.dcc.fc.up.pt/~nam/web/resources/katexp.tgz.

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Authors and Affiliations

  1. CMUP & DCC, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre, 4169-007, Porto, Portugal

    Sabine Broda, Sílvia Cavadas, Miguel Ferreira & Nelma Moreira

Authors
  1. Sabine Broda
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  2. Sílvia Cavadas
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  3. Miguel Ferreira
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  4. Nelma Moreira
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Correspondence to Sabine Broda .

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Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Frank Drewes

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Broda, S., Cavadas, S., Ferreira, M., Moreira, N. (2015). Deciding Synchronous Kleene Algebra with Derivatives. In: Drewes, F. (eds) Implementation and Application of Automata. CIAA 2015. Lecture Notes in Computer Science(), vol 9223. Springer, Cham. https://doi.org/10.1007/978-3-319-22360-5_5

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  • DOI: https://doi.org/10.1007/978-3-319-22360-5_5

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