Specification, testing and implementation relations for symbolic-probabilistic systems

We consider the specification and testing of systems where probabilistic information is not given by means of fixed values but as intervals of probabilities. We will use an extension of the finite state machines model where choices among transitions labelled by the same input action are probabilistically resolved. We will introduce our notion of test and we will define how tests are applied to implementations under test. We will also present implementation relations to assess the conformance, up to a level of confidence, of an implementation to a specification. In order to define these relations we will take finite samples of executions of the implementation and compare them with the probabilistic constraints imposed by the specification. Finally, we will give an algorithm for deriving sound and complete test suites.

[1]  Manuel Núñez,et al.  An Overview of Probabilistic Process Algebras and their Equivalences , 2004, Validation of Stochastic Systems.

[2]  Thomas J. Ostrand,et al.  Black‐Box Testing , 2002 .

[3]  David de Frutos-Escrig,et al.  Testing Semantics for Probabilistic LOTOS , 1995, FORTE.

[4]  Glenford J. Myers,et al.  Art of Software Testing , 1979 .

[5]  Jos C. M. Baeten,et al.  Process Algebra with Timing , 2002, Monographs in Theoretical Computer Science. An EATCS Series.

[6]  Wang Yi,et al.  Testing Probabilistic and Nondeterministic Processes , 1992, PSTV.

[7]  Mario Bravetti,et al.  Discrete time generative-reactive probabilistic processes with different advancing speeds , 2003, Theor. Comput. Sci..

[8]  Manuel Núñez,et al.  Algebraic theory of probabilistic processes , 2003, J. Log. Algebraic Methods Program..

[9]  Manuel Núñez,et al.  Testing of Symbolic-Probabilistic Systems , 2004, International Workshop on Formal Approaches to Testing of Software.

[10]  Rocco De Nicola,et al.  Testing Equivalences for Processes , 1984, Theor. Comput. Sci..

[11]  Frits W. Vaandrager,et al.  A Testing Scenario for Probabilistic Automata , 2003, ICALP.

[12]  A. W. Roscoe,et al.  A Timed Model for Communicating Sequential Processes , 1986, Theor. Comput. Sci..

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

[14]  Bernhard Steffen,et al.  Reactive, Generative and Stratified Models of Probabilistic Processes , 1995, Inf. Comput..

[15]  Keith A. Bartlett,et al.  A note on reliable full-duplex transmission over half-duplex links , 1969, Commun. ACM.

[16]  Roberto Segala,et al.  Testing Probabilistic Automata , 1996, CONCUR.

[17]  Manuel Núñez,et al.  Encoding PAMR into (Timed) EFSMs , 2002, FORTE.

[18]  Rance Cleaveland,et al.  Testing Preorders for Probabilistic Processes , 1992, Inf. Comput..

[19]  Rance Cleaveland,et al.  Priority in Process Algebra , 2001, Handbook of Process Algebra.

[20]  Manuel Núñez,et al.  Towards Testing Stochastic Timed Systems , 2003, FORTE.

[21]  Valentín Valero Ruiz,et al.  Algebraic theory of probabilistic and nondeterministic processes , 2003, J. Log. Algebraic Methods Program..

[22]  Matthew Hennessy,et al.  Algebraic theory of processes , 1988, MIT Press series in the foundations of computing.

[23]  Ivan Christoff,et al.  Testing Equivalences and Fully Abstract Models for Probabilistic Processes , 1990, CONCUR.

[24]  Jan Tretmans,et al.  Test Generation with Inputs, Outputs and Repetitive Quiescence , 1996, Softw. Concepts Tools.

[25]  Wang Yi,et al.  Probabilistic Extensions of Process Algebras , 2001, Handbook of Process Algebra.

[26]  Joseph Sifakis,et al.  An Overview and Synthesis on Timed Process Algebras , 1991, REX Workshop.