Implementation Relations for Stochastic Finite State Machines
We present a timed extension of the classical finite state machines model where time is introduced in two ways. On the one hand, timeouts can be specified, that is, we can express that if an input action is not received before a fix amount of time then the machine will change its state. On the other hand, we can associate time with the performance of actions. In this case, time will be given by means of random variables. Intuitively, we will not have conditions such as “the action a takes t time units to be performed” but conditions such as “the action a will be completed before time t with probability p.” In addition to introducing the new language, we present several conformance relations to relate implementations and specifications that are defined in terms of our new notion of stochastic finite state machine.
KeywordsState Machine Finite State Machine Input Action Process Algebra Stochastic Evolution
Unable to display preview. Download preview PDF.
- [CGP00]Clarke, E.M., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (2000)Google Scholar
- [CL97]Clarke, D., Lee, I.: Automatic generation of tests for timing constraints from requirements. In: 3rd Workshop on Object-Oriented Real-Time Dependable Systems (1997)Google Scholar
- [Her98]Hermanns, H.: Interactive Markov Chains. PhD thesis, Universität Erlangen-Nürnberg (1998)Google Scholar
- [HNTC99]Higashino, T., Nakata, A., Taniguchi, K., Cavalli, A.: Generating test cases for a timed I/O automaton model. In: 12th Workshop on Testing of Communicating Systems, pp. 197–214. Kluwer Academic Publishers, Dordrecht (1999)Google Scholar
- [NR01]Núñez, M., Rodríguez, I.: PAMR: A process algebra for the management of resources in concurrent systems. In: Núñez, M., Rodríguez, I. (eds.) FORTE 2001, pp. 169–185. Kluwer Academic Publishers, Dordrecht (2001)Google Scholar
- [NS91]Nicollin, X., Sifakis, J.: An overview and synthesis on timed process algebras. In: Larsen, K.G., Skou, A. (eds.) CAV 1991. LNCS, vol. 575, pp. 376–398. Springer, Heidelberg (1992)Google Scholar