Rooted branching bisimulation as a congruence for probabilistic transition systems
We propose a probabilistic transition system specification format, referred to as probabilistic RBB safe, for which rooted branching bisimulation is a congruence. The congruence theorem is based on the approach of Fokkink for the qualitative case. For this to work, the theory of transition system sp...
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| Published in: | Electronic proceedings in theoretical computer science Vol. 194; no. Proc. QAPL 2015; pp. 79 - 94 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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28-09-2015
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| Abstract | We propose a probabilistic transition system specification format, referred to as probabilistic RBB safe, for which rooted branching bisimulation is a congruence. The congruence theorem is based on the approach of Fokkink for the qualitative case. For this to work, the theory of transition system specifications in the setting of labeled transition systems needs to be extended to deal with probability distributions, both syntactically and semantically. We provide a scheduler-free characterization of probabilistic branching bisimulation as adapted from work of Andova et al. for the alternating model. Counter examples are given to justify the various conditions required by the format. |
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| AbstractList | We propose a probabilistic transition system specification format, referred to as probabilistic RBB safe, for which rooted branching bisimulation is a congruence. The congruence theorem is based on the approach of Fokkink for the qualitative case. For this to work, the theory of transition system specifications in the setting of labeled transition systems needs to be extended to deal with probability distributions, both syntactically and semantically. We provide a scheduler-free characterization of probabilistic branching bisimulation as adapted from work of Andova et al. for the alternating model. Counter examples are given to justify the various conditions required by the format. |
| Author | Lee, Matias D. de Vink, Erik P. |
| Author_xml | – sequence: 1 givenname: Matias D. surname: Lee fullname: Lee, Matias D. organization: FaMAF, UNC-CONICET, Cordoba – sequence: 2 givenname: Erik P. surname: de Vink fullname: de Vink, Erik P. organization: TU/e, Eindhoven |
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| References | Fokkink (Fok94:tacs) 1994 Miculan (MP14) 2014 Eisentraut (EHKTZ2013) 2013 Fokkink (Fok00) 2000; 60 Hansson (Han91:phd) 1991 Andova (AGT2012) 2012; 413 Groote (GV92) 1992; 100 van Glabbeek (vanG05) 2005 Aceto (AFV99:handbook) 1999 Aceto (ABV94:ic) 1994; 111 van Glabbeek (vG04) 2004; 60-61 Hermanns (HT12) 2012; 18 Lee (LGD12) 2012 Segala (SL95) 1995; 2 Bol (BG96) 1996; 43 Bloom (BIM95) 1995; 42 Klin (Kli09:mosses) 2009 Klin (KS13:ic) 2013; 227 Mousavi (MRG07) 2007; 373 Castiglioni (CLT14:fi) 2014; 135 D'Argenio (DGL14) 2014 Groote (Gro93) 1993; 118 Fokkink (FV98) 1998; 146 Bloom (Bloom95) 1995; 146 Segala (Seg95a) 1995 Bartels (Bart04) 2004 D'Argenio (DL12) 2012 Baeten (BV04:jlap) 2004; 60–61 Lanotte (LT09) 2009; 10 |
| References_xml | – start-page: 17 volume-title: Proc. QAPL 2014 year: 2014 ident: MP14 article-title: GSOS for non-deterministic processes with quantitative aspects doi: 10.4204/EPTCS.154.2 contributor: fullname: Miculan – start-page: 72 volume-title: Proc. QEST year: 2013 ident: EHKTZ2013 article-title: Deciding Bisimilarities on Distributions doi: 10.1007/978-3-642-40196-1_6 contributor: fullname: Eisentraut – volume: 18 start-page: 435 volume-title: FSTTCS 2012 year: 2012 ident: HT12 article-title: Deciding Probabilistic Automata Weak Bisimulation in Polynomial Time contributor: fullname: Hermanns – start-page: 452 volume-title: Proc. FOSSACS year: 2012 ident: DL12 article-title: Probabilistic transition system specification: Congruence and full abstraction of bisimulation doi: 10.1007/978-3-642-28729-9_30 contributor: fullname: D'Argenio – start-page: 197 volume-title: Handbook of Process Algebra year: 1999 ident: AFV99:handbook contributor: fullname: Aceto – volume-title: On Generalised Coinduction and Probabilistic Specification Formats year: 2004 ident: Bart04 contributor: fullname: Bartels – volume-title: Time and probability in formal design of distributed systems year: 1991 ident: Han91:phd contributor: fullname: Hansson – volume: 60–61 start-page: 323 year: 2004 ident: BV04:jlap article-title: Axiomatizing GSOS with Termination publication-title: Journal of Logic and Algebraic Programming doi: 10.1016/j.jlap.2004.03.001 contributor: fullname: Baeten – volume: 146 start-page: 24 year: 1998 ident: FV98 article-title: A Conservative Look at Operational Semantics with Variable Binding publication-title: Information and Computation doi: 10.1006/inco.1998.2729 contributor: fullname: Fokkink – volume: 10 start-page: 1 year: 2009 ident: LT09 article-title: Probabilistic bisimulation as a congruence publication-title: ACM Transactions on Computational Logic doi: 10.1145/1462179.1462181 contributor: fullname: Lanotte – volume: 373 start-page: 238 year: 2007 ident: MRG07 article-title: SOS formats and meta-theory: 20 years after publication-title: Theoretical Computer Science doi: 10.1016/j.tcs.2006.12.019 contributor: fullname: Mousavi – start-page: 115 volume-title: Proc. EXPRESS/SOS year: 2012 ident: LGD12 article-title: Tree rules in probabilistic transition system specifications with negative and quantitative premises doi: 10.4204/EPTCS.89.9 contributor: fullname: Lee – start-page: 121 volume-title: Semantics and Algebraic Specification year: 2009 ident: Kli09:mosses article-title: Structural Operational Semantics for Weighted Transition Systems doi: 10.1007/978-3-642-04164-8_7 contributor: fullname: Klin – volume: 111 start-page: 1 year: 1994 ident: ABV94:ic article-title: Turning SOS Rules into Equations publication-title: Information and Computation doi: 10.1006/inco.1994.1040 contributor: fullname: Aceto – volume: 135 start-page: 355 year: 2014 ident: CLT14:fi article-title: A Specification Format for Rooted Branching Bisimulation publication-title: Fundamenta Informaticae doi: 10.3233/FI-2014-1128 contributor: fullname: Castiglioni – volume: 100 start-page: 202 year: 1992 ident: GV92 article-title: Structured Operational Semantics and Bisimulation as a Congruence publication-title: Information and Computation doi: 10.1016/0890-5401(92)90013-6 contributor: fullname: Groote – start-page: 289 volume-title: Proc. FoSSACS year: 2014 ident: DGL14 article-title: Axiomatizing bisimulation equivalences and metrics from probabilistic SOS rules doi: 10.1007/978-3-642-54830-7_19 contributor: fullname: D'Argenio – volume: 227 start-page: 58 year: 2013 ident: KS13:ic article-title: Structural operational semantics for stochastic and weighted transition systems publication-title: Information and Computation doi: 10.1016/j.ic.2013.04.001 contributor: fullname: Klin – volume: 60 start-page: 13 year: 2000 ident: Fok00 article-title: Rooted Branching Bisimulation as a Congruence publication-title: Journal of Computer and System Sciences doi: 10.1006/jcss.1999.1663 contributor: fullname: Fokkink – volume-title: Modeling and Verification of Randomized Distributed Real-Time Systems year: 1995 ident: Seg95a contributor: fullname: Segala – volume: 413 start-page: 58 year: 2012 ident: AGT2012 article-title: Branching bisimulation congruence for probabilistic systems publication-title: Theoretical Computer Science doi: 10.1016/j.tcs.2011.07.020 contributor: fullname: Andova – volume: 43 start-page: 863 year: 1996 ident: BG96 article-title: The meaning of negative premises in transition system specifications publication-title: Journal of the ACM doi: 10.1145/234752.234756 contributor: fullname: Bol – volume: 2 start-page: 250 year: 1995 ident: SL95 article-title: Probabilistic simulations for probabilistic processes publication-title: Nordic Journal of Computing contributor: fullname: Segala – volume: 118 start-page: 263 year: 1993 ident: Gro93 article-title: Transition system specifications with negative premises publication-title: Theoretical Computer Science doi: 10.1016/0304-3975(93)90111-6 contributor: fullname: Groote – start-page: 440 volume-title: Proc. TACS 1994 year: 1994 ident: Fok94:tacs article-title: The tyft/tyxt Format Reduces to Tree Rules doi: 10.1007/3-540-57887-0_109 contributor: fullname: Fokkink – start-page: 318 volume-title: Proc. ICTAC 2005 year: 2005 ident: vanG05 article-title: On cool congruence formats for weak bisimulations doi: 10.1007/11560647_21 contributor: fullname: van Glabbeek – volume: 60-61 start-page: 229 year: 2004 ident: vG04 article-title: The Meaning of Negative Premises in Transition System Specifications II publication-title: Journal of Logic and Algebraic Programming doi: 10.1016/j.jlap.2004.03.007 contributor: fullname: van Glabbeek – volume: 42 start-page: 232 year: 1995 ident: BIM95 article-title: Bisimulation can't be traced publication-title: Journal of the ACM doi: 10.1145/200836.200876 contributor: fullname: Bloom – volume: 146 start-page: 25 year: 1995 ident: Bloom95 article-title: Structural operational semantics for weak bisimulations publication-title: Theoretical Computer Science doi: 10.1016/0304-3975(94)00152-9 contributor: fullname: Bloom |
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