Abstract
In this paper we define a probabilistic testing semantics which can be used to alternatively characterize fair testing. The key idea is to define a probabilistic semantics in such a way that two non-probabilistic processes are fair equivalent if any probabilistic version of both processes are equivalent in our probabilistic testing semantics. In order to get this result we define a simple probabilistic must semantics by saying that a probabilistic process must pass a test if the probability with which the process passes the test equals 1. Finally, we present an algorithm for deciding whether the probability with which a finite-state process passes a finite-state test equals 1. Alternatively, this algorithm can be used for computing whether a finite-state process fairly passes a finite-state test.
Chapter PDF
Similar content being viewed by others
References
Baeten, J., Bergstra, J., and Klop, J. (1987). On the consistency of Koomen’s fair abstraction rule. Theoretical Computer Science, 51 (1–2): 129–176.
Bergstra et al., 1987] Bergstra, J., J.W.Klop, and Olderog, E. (1987). Failures without chaos: A new process semantics for fair abstraction. In Formal Description of Programming Concepts III, pages 77–103. Elsevier.
Brinksma, 1988] Brinksma, E. (1988). A theory for the derivation of tests. In Pro- tocol Specification, Testing and Verification VIII, pages 63–74. North Holland.
Brinksma et al., 1995] Brinksma, E., Rensink, A., and Vogler, W. (1995). Fair testing. In CONCUR’95, LNCS 962, pages 313–327. Springer.
Brinksma et al., 1996] Brinksma, E., Rensink, A., and Vogler, W. (1996). Applications of fair testing. In Formal Description Techniques for Distributed Systems and Communication Protocols (IX), and Protocol Specification, Testing, and Verification (X VI), pages 145–160. Chapman & Hall.
Brookes, S., Hoare, C., and Roscoe, A. (1984). A theory of communicating sequential processes. Journal of the ACM, 31 (3): 560–599.
Christoff, 1990] Christoff, I. (1990). Testing equivalences and fully abstract models for probabilistic processes. In CONCUR’90, LNCS 458, pages 126–140. Springer.
Cleaveland et al., 1996] Cleaveland, R., Lee, I., Lewis, P., and Smolka, S. (1996). A theory of testing for soft real-time processes. In 8th International Conference on Software Engineering and Knowledge Engineering.
Cleaveland et al., 1992] Cleaveland, R., Smolka, S., and Zwarico, A. (1992). Testing preorders for probabilistic processes. In 19th ICALP, LNCS 623, pages 708–719. Springer.
Costa, G. and Stirling, C. (1987). Weak and strong fairness in CCS. Information and Computation, 87: 207–244.
D’Argenio et al., 1999] D’Argenio, P. R., Hermanns, H., and Katoen, J.-P. (1999). On generative parallel composition. In PROBMIV’98, Electronics Notes in Theoretical Computer Science 21. Elsevier.
de Frutos-Escrig et al., 1997] de Frutos-Escrig, D., Liana-Díaz, L., and Núnez, M. (1997). Friendly testing as a conformance relation. In Formal Description Techniques for Distributed Systems and Communication Protocols (X), and Protocol Specification, Testing, and Verification (XVII), pages 283–298. Chapman & Hall.
de Frutos-Escrig, D., Liana-Diaz, L., and Núnez, M. (1998). An invitation to friendly testing. Journal of Computer Science and Technology, 13 (6): 531–545.
de Nicola, R. and Hennessy, M. (1984). Testing equivalences for processes. Theoretical Computer Science, 34: 83–133.
Francez, N. (1986). Fairness. Springer.
Gregorio et al., 1997] Gregorio, C., Liana, L., Núnez, M., and Palao, P. (1997). Testing semantics for a probabilistic-timed process algebra. In 4th International AMAST Workshop on Real-Time Systems, Concurrent, and Distributed Software, LNCS 1231, pages 353–367. Springer.
Gregorio, C. and Núnez, M. (1996). Specifying and verifying the Alternating Bit Protocol with Probabilistic-Timed LOTOS. In COST 247 International Workshop on Applied Formal Methods in System Design, pages 38–50.
Gregorio and Núnez, 1999] Gregorio, C. and Núnez, M. (1999). Denotational semantics for probabilistic refusal testing. In PROBMIV’98, Electronics Notes in Theoretical Computer Science 21. Elsevier.
Hennessy, M. (1987). An algebraic theory of fair asynchronous communicating processes. Theoretical Computer Science, 49: 121–143.
Hennessy, M. (1988). Algebraic Theory of Processes. MIT Press.
Koomen, C. (1985). Algebraic specification and verification of communications protocols. Science of Computer Programming, 5: 1–36.
Kumar, K. N., Cleaveland, R., and Smolka, S. (1998). Infinite probabilistic and nonprobabilistic testing. In 18th Conference on Foundations of Software Technology and Theoretical Computer Science, LNCS 1530, pages 209220.
Milner, 1981] Milner, R. (1981). A modal characterization of observable machine-behaviour. In 6th CAAP, LNCS 112, pages 25–34. Springer.
Natarajan and Cleaveland, 1995] Natarajan, V. and Cleaveland, R. (1995). Diver- gence and fair testing. In 22nd ICALP, LNCS 944, pages 648–659. Springer.
Núnez, 1999] Núnez, M. (1999). An axiomatization of probabilistic testing. In 5th AMAST Workshop on Real-Time and Probabilistic Systems, LNCS 1601, pages 130–150. Springer.
Núnez and de Frutos, 1995] Núnez, M. and de Frutos, D. (1995). Testing semantics for probabilistic LOTOS. In Formal Description Techniques VIII, pages 365–380. Chapman & Hall.
Núnez et al., 1995] Núnez, M., de Frutos, D., and Liana, L. (1995). Acceptance trees for probabilistic processes. In CONCUR’95, LNCS 962, pages 249–263. Springer.
Rupérez, D. (1997). Una semantica de pruebas fair mediante un modelo probabilístico. Master Thesis. Dept. Sistemas Informaticos y Programación. Universidad Complutense de Madrid.
Tretmans, J. (1996). Conformance testing with labelled transition systems: Implementation relations and test generation. Computer Networks and ISDN Systems, 29: 49–79.
Yuen et al., 1994] Yuen, S., Cleaveland, R., Dayar, Z., and Smolka, S. (1994). Fully abstract characterizations of testing preorders for probabilistic processes. In CONCUR’94, LNCS 836, pages 497–512. Springer.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Núñez, M., Rupérez, D. (1999). Fair Testing Through Probabilistic Testing. In: Wu, J., Chanson, S.T., Gao, Q. (eds) Formal Methods for Protocol Engineering and Distributed Systems. PSTV FORTE 1999 1999. IFIP Advances in Information and Communication Technology, vol 28. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35578-8_8
Download citation
DOI: https://doi.org/10.1007/978-0-387-35578-8_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-5270-0
Online ISBN: 978-0-387-35578-8
eBook Packages: Springer Book Archive