Abstract
We introduce three new notions of infinite testing for probabilistic processes, namely, simple, Büchi and fair infinite testing. We carefully examine their distinguishing power and show that all three have the same power as finite tests. We also consider Büchi tests in the non-probabilistic setting and show that they have the same distinguishing power as finite tests. Finally, we show that finite probabilistic tests are stronger than nondeterministic fair tests.
(Research supported in part by NSF Grant CCR-9505562 and AFOSR Grants F49620-93-1-0250 and F49620-95-1-0508.)
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Brinksma, E., Rensink, A., Vogler, W.: Fair testing. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962. Springer, Heidelberg (1995)
Cleaveland, R., Dayar, Z., Smolka, S.A., Yuen, S., Zwarico, A.: Testing preorders for probabilistic processes. Information and Computation (1998) (to Appear)
De Nicola, R., Hennessy, M.C.B.: Testing equivalences for processes. Theoretical Computer Science 34, 83–133 (1983)
Feller, W.: Probability Theory and its Applications. John Wiley and Sons, Chichester (1950)
van Glabbeek, R.J., Smolka, S.A., Steffen, B.: Reactive, generative, and stratified models of probabilistic processes. Information and Computation 121(1), 59–80 (1995)
Hennessy, M.C.B.: Algebraic Theory of Processes. MIT Press, Boston (1988)
Jonsson, B., Yi, W.: Compositional testing preorders for probabilistic processes. In: Proceedings of LICS 1995, pp. 431–441 (1995)
Natarajan, V., Cleaveland, R.: Divergence and fair testing. In: Fülöp, Z., Gecseg, F. (eds.) ICALP 1995. LNCS, vol. 944. Springer, Heidelberg (1995)
Segala, R.: Testing probabilistic automata. In: Sassone, V., Montanari, U. (eds.) CONCUR 1996. LNCS, vol. 1119. Springer, Heidelberg (1996)
Shiryayev, A.N.: Probability. Graduate Texts in Mathematics. Springer, Heidelberg (1980)
Wu, S.-H., Smolka, S.A., Stark, E.W.: Composition and behaviors of probabilistic I/O automata. Theoretical Computer Science 176 (1997)
Yi, W., Larsen, K.G.: Testing probabilistic and nondeterministic processes. In: Protocol Specification, Testing and Verification, vol. XII, pp. 47–61. North-Holland (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kumar, K.N., Cleaveland, R., Smolka, S.A. (1998). Infinite Probabilistic and Nonprobabilistic Testing. In: Arvind, V., Ramanujam, S. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1998. Lecture Notes in Computer Science, vol 1530. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49382-2_19
Download citation
DOI: https://doi.org/10.1007/978-3-540-49382-2_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65384-4
Online ISBN: 978-3-540-49382-2
eBook Packages: Springer Book Archive