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International Workshop on Coalgebraic Methods in Computer Science

CMCS 2012: Coalgebraic Methods in Computer Science pp 109–129Cite as

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Trace Semantics via Determinization

Trace Semantics via Determinization

  • Bart Jacobs18,
  • Alexandra Silva18 &
  • Ana Sokolova19 
  • Conference paper
  • 657 Accesses

  • 13 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7399)

Abstract

This paper takes a fresh look at the topic of trace semantics in the theory of coalgebras. The first development of coalgebraic trace semantics used final coalgebras in Kleisli categories, stemming from an initial algebra in the underlying category. This approach requires some non-trivial assumptions, like dcpo enrichment, which do not always hold, even in cases where one can reasonably speak of traces (like for weighted automata). More recently, it has been noticed that trace semantics can also arise by first performing a determinization construction. In this paper, we develop a systematic approach, in which the two approaches correspond to different orders of composing a functor and a monad, and accordingly, to different distributive laws. The relevant final coalgebra that gives rise to trace semantics does not live in a Kleisli category, but more generally, in a category of Eilenberg-Moore algebras. In order to exploit its finality, we identify an extension operation, that changes the state space of a coalgebra into a free algebra, which abstractly captures determinization of automata. Notably, we show that the two different views on trace semantics are equivalent, in the examples where both approaches are applicable.

Keywords

  • Natural Transformation
  • Free Algebra
  • Forgetful Functor
  • Deterministic Automaton
  • Extension Semantic

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Author information

Authors and Affiliations

  1. Institute for Computing and Information Sciences, Radboud University, Nijmegen, The Netherlands

    Bart Jacobs & Alexandra Silva

  2. Department of Computer Sciences, University of Salzburg, Austria

    Ana Sokolova

Authors
  1. Bart Jacobs
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  2. Alexandra Silva
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  3. Ana Sokolova
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Editor information

Editors and Affiliations

  1. Research School of Information Sciences and Engineering, The Australian National University, 0200, Canberra, ACT, Australia

    Dirk Pattinson

  2. Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058, Erlangen, Germany

    Lutz Schröder

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Cite this paper

Jacobs, B., Silva, A., Sokolova, A. (2012). Trace Semantics via Determinization. In: Pattinson, D., Schröder, L. (eds) Coalgebraic Methods in Computer Science. CMCS 2012. Lecture Notes in Computer Science, vol 7399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32784-1_7

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  • DOI: https://doi.org/10.1007/978-3-642-32784-1_7

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