Bisimulation and simulation algorithms on probabilistic transition systems by abstract interpretation

We show how bisimulation equivalence and simulation preorder on probabilistic LTSs (PLTSs), namely the main behavioural relations on probabilistic nondeterministic processes, can be characterized by abstract interpretation. Both bisimulation and simulation can be obtained as completions of partitions and preorders, viewed as abstract domains, w.r.t. a pair of concrete functions that encode a PLTS. This approach provides a general framework for designing algorithms that compute bisimulation and simulation on PLTSs. Notably, (i) we show that the standard bisimulation algorithm by Baier et al. (2000) can be viewed as an instance of such a framework and (ii) we design a new efficient simulation algorithm that improves the state of the art.

[1]  Roberto Giacobazzi,et al.  Refining and Compressing Abstract Domains , 1997, ICALP.

[2]  Roberto Giacobazzi,et al.  Incompleteness, Counterexamples, and Refinements in Abstract Model-Checking , 2001, SAS.

[3]  Francesco Ranzato,et al.  An efficient simulation algorithm based on abstract interpretation , 2007, Inf. Comput..

[4]  Robert E. Tarjan,et al.  Three Partition Refinement Algorithms , 1987, SIAM J. Comput..

[5]  Francesco Ranzato,et al.  A New Efficient Simulation Equivalence Algorithm , 2007, 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007).

[6]  Kim G. Larsen,et al.  Bisimulation through Probabilistic Testing , 1991, Inf. Comput..

[7]  Thomas A. Henzinger,et al.  Computing simulations on finite and infinite graphs , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[8]  Bernhard Steffen,et al.  Reactive, generative, and stratified models of probabilistic processes , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[9]  Patrick Cousot,et al.  Systematic design of program analysis frameworks , 1979, POPL.

[10]  Silvia Crafa,et al.  Probabilistic Bisimulation and Simulation Algorithms by Abstract Interpretation , 2011, ICALP.

[11]  Lijun Zhang,et al.  Flow Faster: Efficient Decision Algorithms for Probabilistic Simulations , 2007, TACAS.

[12]  Abbas Edalat,et al.  Bisimulation for Labelled Markov Processes , 2002, Inf. Comput..

[13]  Lijun Zhang.  A Space-Efficient Probabilistic Simulation Algorithm , 2008, CONCUR.

[14]  Francesco Ranzato,et al.  Generalized Strong Preservation by Abstract Interpretation , 2004, J. Log. Comput..

[15]  Lijun Zhang,et al.  Decision algorithms for probabilistic simulations , 2009 .

[16]  Vincent Danos,et al.  Labelled Markov Processes: Stronger and Faster Approximations , 2004, Electron. Notes Theor. Comput. Sci..

[17]  Patrick Cousot,et al.  Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints , 1977, POPL.

[18]  Christel Baier,et al.  Deciding Bisimilarity and Similarity for Probabilistic Processes , 2000, J. Comput. Syst. Sci..

[19]  Roberto Segala,et al.  Logical Characterizations of Bisimulations for Discrete Probabilistic Systems , 2007, FoSSaCS.

[20]  Nancy A. Lynch,et al.  Probabilistic Simulations for Probabilistic Processes , 1994, Nord. J. Comput..