Abstract
We use modal logic as a framework for coalgebraic trace semantics, and show the flexibility of the approach with concrete examples such as the language semantics of weighted, alternating and tree automata. We provide a sufficient condition under which a logical semantics coincides with the trace semantics obtained via a given determinization construction. Finally, we consider a condition that guarantees the existence of a canonical determinization procedure that is correct with respect to a given logical semantics. That procedure is closely related to Brzozowski’s minimization algorithm.
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Adámek, J., Bonchi, F., Hülsbusch, M., König, B., Milius, S., Silva, A.: A coalgebraic perspective on minimization and determinization. In: Birkedal, L. (ed.) FOSSACS 2012. LNCS, vol. 7213, pp. 58–73. Springer, Heidelberg (2012)
Bezhanishvili, N., Kupke, C., Panangaden, P.: Minimization via duality. In: Ong, L., de Queiroz, R. (eds.) WoLLIC 2012. LNCS, vol. 7456, pp. 191–205. Springer, Heidelberg (2012)
Bonchi, F., Bonsangue, M.M., Hansen, H.H., Panangaden, P., Rutten, J.J.M.M., Silva, A.: Algebra-coalgebra duality in Brzozowski’s minimization algorithm. ACM Trans. Comput. Log. 15(1), 3 (2014)
Brzozowski, J.: Canonical regular expressions and minimal state graphs for definite events. Mathematical Theory of Automata 12, 529–561 (1962)
Cîrstea, C.: From branching to linear time, coalgebraically. In: Procs. FICS 2013. EPTCS, vol. 126, pp. 11–27 (2013)
Cîrstea, C.: A coalgebraic approach to linear-time logics. In: Muscholl, A. (ed.) FOSSACS 2014 (ETAPS). LNCS, vol. 8412, pp. 426–440. Springer, Heidelberg (2014)
Cîrstea, C., Pattinson, D.: Modular construction of modal logics. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 258–275. Springer, Heidelberg (2004)
Goncharov, S.: Trace semantics via generic observations. In: Heckel, R., Milius, S. (eds.) CALCO 2013. LNCS, vol. 8089, pp. 158–174. Springer, Heidelberg (2013)
Hasuo, I., Jacobs, B., Sokolova, A.: Generic trace semantics via coinduction. Log. Meth. Comp. Sci. 3(4) (2007)
Hermida, C., Jacobs, B.: Structural induction and coinduction in a fibrational setting. Inf. and Comp. 145, 107–152 (1997)
Jacobs, B.: Introduction to coalgebra. Towards mathematics of states and observations, Draft (2014)
Jacobs, B., Silva, A., Sokolova, A.: Trace semantics via determinization. J. Comp. and Sys. Sci. (2014) (to appear)
Jacobs, B., Sokolova, A.: Exemplaric expressivity of modal logics. J. Log. and Comput. 20(5), 1041–1068 (2010)
Kissig, C., Kurz, A.: Generic trace logics. CoRR, abs/1103.3239 (2011)
Klin, B.: Coalgebraic modal logic beyond sets. ENTCS 173, 177–201 (2007)
Kupke, C., Pattinson, D.: Coalgebraic semantics of modal logics: An overview. Theor. Comput. Sci. 412(38), 5070–5094 (2011)
Kurz, A., Milius, S., Pattinson, D., Schröder, L.: Simplified coalgebraic trace equivalence. CoRR, abs/1410.2463 (2014)
Lenisa, M., Power, J., Watanabe, H.: Category theory for operational semantics. Theor. Comput. Sci. 327(1-2), 135–154 (2004)
Lane, S.M.: Categories for the working mathematician, vol. 5. Springer (1998)
Pavlovic, D., Mislove, M.W., Worrell, J.B.: Testing semantics: Connecting processes and process logics. In: Johnson, M., Vene, V. (eds.) AMAST 2006. LNCS, vol. 4019, pp. 308–322. Springer, Heidelberg (2006)
Power, J., Turi, D.: A coalgebraic foundation for linear time semantics. ENTCS 29, 259–274 (1999)
Rutten, J.J.M.M.: Universal coalgebra: A theory of systems. Theor. Comput. Sci. 249(1), 3–80 (2000)
Schröder, L., Pattinson, D.: Modular algorithms for heterogeneous modal logics via multi-sorted coalgebra. Math. Struct. in Comp. Sci. 21(2), 235–266 (2011)
Silva, A., Bonchi, F., Bonsangue, M.M., Rutten, J.J.M.M.: Generalizing determinization from automata to coalgebras. Log. Meth. Comp. Sci. 9(1) (2013)
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Klin, B., Rot, J. (2015). Coalgebraic Trace Semantics via Forgetful Logics. In: Pitts, A. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2015. Lecture Notes in Computer Science(), vol 9034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46678-0_10
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DOI: https://doi.org/10.1007/978-3-662-46678-0_10
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