Abstract
In automata theory, a machine transitions from one state to the next when it reads an input symbol. It is common to also allow an automaton to transition without input, via an ε-transition. These ε-transitions are convenient, e.g., when one defines the composition of automata. However, they are not necessary, and can be eliminated. Such ε-elimination procedures have been studied separately for different types of automata, including non-deterministic and weighted automata.
It has been noted by Hasuo that it is possible to give a coalgebraic account of ε-elimination for some automata using trace semantics (as defined by Hasuo, Jacobs and Sokolova).
In this paper, we give a detailed description of the ε-elimination procedure via trace semantics (missing in the literature). We apply this framework to several types of automata, and explore its boundary.
In particular, we show that is possible (by careful choice of a monad) to define an ε-removal procedure for all weighted automata over the positive reals (and certain other semirings). Our definition extends the recent proposals by Sakarovitch and Lombardy for these semirings.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bonchi, F., Bonsangue, M., Boreale, M., Rutten, J., Silva, A.: A coalgebraic perspective on linear weighted automata. Inf. Comput. 211, 77–105 (2012)
Bonchi, F., Bonsangue, M., Rutten, J., Silva, A.: Brzozowski’s algorithm (co)algebraically. In: Constable, R.L., Silva, A. (eds.) Logic and Program Semantics. LNCS, vol. 7230, pp. 12–23. Springer, Heidelberg (2012)
Bonchi, F., Pous, D.: Checking NFA equivalence with bisimulations up to congruence. In: POPL, pp. 457–468. ACM (2013)
Brengos, T.: Weak bisimulations for coalgebras over ordered functors. In: Baeten, J.C.M., Ball, T., de Boer, F.S. (eds.) TCS 2012. LNCS, vol. 7604, pp. 87–103. Springer, Heidelberg (2012)
Droste, M., Kuich, W., Vogler, W.: Handbook of Weighted Automata. Springer (2009)
Peter Gumm, H., Schröder, T.: Monoid-labeled transition systems. ENTCS 44(1), 185–204 (2001)
Hasuo, I., Jacobs, B., Sokolova, A.: Generic Forward and Backward Simulations. In: Proceedings of JSSST Annual Meeting (2006) (Partly in Japanese)
Hasuo, I., Jacobs, B., Sokolova, A.: Generic Trace Semantics via Coinduction. Logical Methods in Computer Science 3(4) (2007)
Jacobs, B.: From coalgebraic to monoidal traces. ENTCS 264(2), 125–140 (2010)
Jacobs, B., Silva, A., Sokolova, A.: Trace semantics via determinization. In: Pattinson, D., Schröder, L. (eds.) CMCS 2012. LNCS, vol. 7399, pp. 109–129. Springer, Heidelberg (2012)
Kerstan, H., König, B.: Coalgebraic trace semantics for probabilistic transition systems based on measure theory. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 410–424. Springer, Heidelberg (2012)
Lombardy, S., Sakarovitch, J.: The Removal of Weighted ε-Transitions. In: Moreira, N., Reis, R. (eds.) CIAA 2012. LNCS, vol. 7381, pp. 345–352. Springer, Heidelberg (2012)
Milius, S.: On Iteratable Endofunctors. In: CTCS. ENTCS, vol. 69, pp. 287–304. Elsevier (2002)
Mohri, M.: Generic ε-removal algorithm for weighted automata. In: Yu, S., Păun, A. (eds.) CIAA 2000. LNCS, vol. 2088, pp. 230–242. Springer, Heidelberg (2001)
Rutten, J.: Automata and coinduction (an exercise in coalgebra). In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 194–218. Springer, Heidelberg (1998)
Sangiorgi, D.: An introduction to bisimulation and coinduction. Cambridge University Press (2012)
Silva, A., Bonchi, F., Bonsangue, M., Rutten, J.: Generalizing the powerset construction, coalgebraically. In: FSTTCS. LIPIcs, vol. 8, pp. 272–283 (2010)
Silva, A., Bonchi, F., Bonsangue, M., Rutten, J.: Generalizing determinization from automata to coalgebras. LMCS 9(1) (2013)
Silva, A., Westerbaan, B.: A Coalgebraic View of ε-Transitions. Extended abstract, with proofs, http://alexandrasilva.org/files/epsilon-extended.pdf
Sokolova, A., de Vink, E., Woracek, H.: Coalgebraic weak bisimulation for action-type systems. Sci. Ann. Comp. Sci. 19, 93–144 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Silva, A., Westerbaan, B. (2013). A Coalgebraic View of ε-Transitions. In: Heckel, R., Milius, S. (eds) Algebra and Coalgebra in Computer Science. CALCO 2013. Lecture Notes in Computer Science, vol 8089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40206-7_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-40206-7_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40205-0
Online ISBN: 978-3-642-40206-7
eBook Packages: Computer ScienceComputer Science (R0)