Courcoubetis C. and Yannakakis M. [1995], `The complexity of probabilistic veri cation', Journal of the ACM 42(4), 857-907. Home/Search Document Not in Database Summary ACM TOC Related Articles Check |
This paper is cited in the following contexts:
Almost-Certain Eventualities and Abstract Probabilities in.. - McIver, Morgan (2002) (Correct)
.... nondeterminism [1] Indeed it still appears that the luxury of enhancing the logic s expressivity in this way is paid by the complexity in the model checking, for the best known algorithms imply that (in this case) it is quadratic (e.g. de Alfaro and Henzinger [17] Courcoubetis and Yannakakis [18] and Vardi [1] ....
C. Courcoubetis, M. Yannakakis, The complexity of probabilistic veri cation, JACM 42 (4) (1995) 857-907.
Metrics for Labelled Markov Processes - Desharnais, Jagadeesan, al. (2003) (Correct)
....of this paper to systems which have both probability and traditional nondeterminism remains open and is the subject of active research at the moment. The veri cation community has been active in developing model checking tools for probabilistic systems, for example [BLL 96, BdA95, BCHG 97, CY95, HK97] Approximation techniques in the spirit of those of this paper have been explored for hybrid systems [GHJ97] Since the rst appearance of the present work [DGJP99] we have developed a theory of approximation for labelled Markov processes [DGJP00, DGJP03] Before we discuss work speci ....
C. Courcoubetis and M. Yannakakis. The complexity of probabilistic veri cation. Journal of the ACM, 42(4):857-907, 1995.
Classes of Timed Automata and the Undecidability of Universality - Moura, Pinto (2001) (Correct)
....j; z) i MH2 accepts the tuple hz; i; ji, with oracles f and g. We have that U TBA = fz j 8f9g [ 8i 9j H 1 (f; i; j) 8i 9j H 2 (f; g; i; j; z) g. By the normal form theorem [13] U TBA 2 2 . ut 3 Almost Deterministic TBA Almost determinism were considered before for B uchi automata [6, 14] as a means of achieving better complexity bounds for a probabilistic veri cation problem. From the perspective of expressiveness, almost deterministic and nondeterministic B uchi automata de ne the same class of languages. The situation is more interesting for TBA. In section 7 we show that ....
C. Courcoubetis and M. Yannakakis. The complexity of probabilistic veri cation. Journal of the ACM, 42(4):857-907, 1995.
A Logic of Probability With Decidable Model-Checking - Beauquier (2001) (Correct)
....that allow one to say with probability one or with probability greater that zero . Most work related to the veri cation used probalilistic expensions of temporal logics; in these extensions the probabilities can be used in very constraint ways. This work is surveyed, for example in [Han94] and [CY95] Our interest is in predicate logics. A fundamental contribution to the study of predicate logics of probability related to our context was done in [FHM90, Hal90] The paper [FHM90] contains a good survey of previous works on logic analysis of probabilities mainly motivated by the problems of ....
....: Xm ) i (N a ; a; S 0 1 ; S 0 2 ; S 0 m ) j= x 0 ; X 1 ; X 2 ; Xm ) where S 0 i = S i N a for i = 1; 2; m and N a = fn 2 Nj n ag. Past MLO Formulas are de ned in a symmetric way. Note that this is a semantical notion. Below we will use the following theorem from [CY95] Theorem 4.1.7) Theorem 3 Let (t) be a MLO future formula with only one free variable and M be a Finite Probabilistic Process. One can compute for each state s of M , the probability f s that (0) is true in M s at state s. Recall that a set S N is ultimately periodic if there are h; d 2 ....
C. Courcoubetis and M. Yannakakis. The complexity of probabilistic verication. Journal of the ACM, 42:857-907, 1995.
Metrics for Labelled Markov Systems - Desharnais, Jagadeesan, al. (2001) (1 citation) (Correct)
....this paper to systems which have both probability and traditional nondeterminism remains open and is the subject of active research at the moment. The veri cation community has been active in developing model checking tools for probabilistic systems, for example [BLL 96, BdA95, BCHG 97, CY95, HK97] Approximation techniques in the spirit of those of this paper have been explored for hybrid systems [GHJ97] Since the rst 25 appearance of the present work [DGJP99] we have developed a theory of approximation for labelled Markov processes [DGJP00] Before we discuss work speci cally ....
C. Courcoubetis and M. Yannakakis. The complexity of probabilistic verication. Journal of the ACM, 42(4):857-907, 1995.
Randomization Helps in LTL Model Checking - Brim, Cerna, Necesal (2001) (2 citations) (Correct)
....The term probabilistic model checking (or probabilistic veri cation ) refers to a wide range of techniques. There are two ways in which probability features in this area. The rst approach concerns applying model checking to systems which inherently include probabilistic information [11, 4, 1, 2]. The second approach concerns systems which are non probabilistic, but of size which makes exhaustive checking This work has been partially supported by the Grant Agency of Czech Republic grants No. 201 00 1023 and 201 00 0400. PAPM PROBMIV workshop 2001, Aachen, Germany 2001 impractical or ....
C. Courcoubetis and M. Yannakakis. The Complexity of Probabilistic Verication. Journal of the ACM, 42(4):857-907, July 1995.
Approximating Labelled Markov Processes - Desharnais, Jagadeesan, al. (2001) (5 citations) (Correct)
....nets [Mar89, VN92] add Markov chains to the underlying Petri net model. Probabilistic extensions of IO Automata [Seg95, WSS97] have also been developed. The veri cation community has been active in developing model checking tools for probabilistic systems, for example [BLL 96, BdA95, BK97, CY95, HK97] By and large, the above work focuses on discrete state systems. The other investigation that we are aware of apart from our earlier papers [BDEP97, DEP98] into continuous state spaces was by deVink and Rutten [dVR97] They de ne a probabilistic transition system as a coalgebra of a ....
C. Courcoubetis and M. Yannakakis. The complexity of probabilistic verication. Journal of the ACM, 42(4):857-907, 1995.
Model Checking Probabilistic Systems - Notes to accompany.. - Kwiatkowska (2000) (Correct)
.... mention SPIN and FDR) There have also been encouraging developments in model checking of real time and hybrid systems [10, 13] One area that is lagging behind as far as experimental work is concerned, despite the fact that the fundamental veri cation algorithms have been known for over a decade [44, 28, 41, 18], is model checking of probabilistic systems. Many systems currently being designed, for example communication protocols, multimedia systems, randomized distributed algorithms, require probabilistic analysis performed in addition to the conventional, qualitative, checks involving temporal logic ....
....of quality of service characteristics such as long run average, resource utilization, etc. 2 Model checking of probabilistic systems The rst approaches to adding probability to systems and temporal logic were qualitative, i.e. required satisfaction almost always (with probability 1) see e.g. [44, 28, 41, 42, 18]. It turns out that probabilistic analysis in such cases can be reduced to conventional nonprobabilistic analysis, without the need to compute the exact probabilities. The quantitative approach, where the actual probability of an event must be calculated, is more involved, and also necessary for ....
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C. Courcoubetis and M. Yannakakis. The complexity of probabilistic verication. Journal of the ACM, 42(4):857-907, 1995.
Fairness, Computable Fairness, and Randomness - Jaeger (Correct)
....In this section we introduce the basic terminology we shall need. In most works related to the issues we are here dealing with, models for systems are introduced that combine nondeterminism with randomness (e.g. concurrent Markov chains (Vardi 1985) or similar models (Pnueli Zuck 1993, Courcoubetis Yannakakis 1995, Baier Kwiatkowska 1998) For the study of our question how concepts of fairness relate to probabilistic behavior, however, we only need the following two very basic models of nondeterministic, respectively probabilistic, transition systems. Here and in the sequel we use P(S) to denote the ....
Courcoubetis, C. & Yannakakis, M. (1995), `The complexity of probabilistic verication', Journal of the ACM 42(4), 857-907.
Symbolic Model Checking of Probabilistic Processes .. - de Alfaro.. (2000) (1 citation) (Correct)
....step of [19] 2 Concurrent Probabilistic Systems In this section, we brie y summarise our underlying model for concurrent probabilistic systems; the reader is referred to [5, 2] for more details. Our model is based on Markov decision processes , and is similar to Concurrent Markov Chains of [32, 16] and simple deterministic automata of [29] Some familiarity with Markov chains and probability theory is assumed. Concurrent probabilistic systems generalise ordinary Markov chains in that they allow a nondeterministic choice between possibly several probability distributions in a given state. ....
....iteration. 4.1 Probability 1 Precomputation Step The model checking algorithm for until properties given below can be improved by pre computing the set of all states from which the formula holds with maximal probability 1. The algorithm for this precomputation step is based on results of [15, 16] and can be derived from that in [19] for computing the set of states that can reach a goal with probability 1. We have here adapted it to until formulas. For any Z 0 ; Z 1 S let Pre(Z 0 ; Z 1 ) be the set of states de ned by: Pre(Z 0 ; Z 1 ) fx j 9p 2 Steps(x) 8y(p(y) 0 y 2 Z 0 ) ....
C. Courcoubetis and M. Yannakakis. The complexity of probabilistic verication. Journal of the ACM, 42(4):857-907, 1995.
On the Verification of Nondeterministic Automata.. - Moura, Pinto (1999) (Correct)
....TA are not closed under complementation [3] so that one must resort to some other technique to cope with the nondeterminism in the speci cation. For instance, in the discrete time domain, where the system is a Markov chain and the speci cation an automaton, Courcoubetis and Yannakakis [7] solved a more general problem with the usual subset construction. But, for TA, it was not clear in [2] how one could apply such a construction, and also carry through the probabilistic analysis. In this paper, we show that a subset construction on the states (location plus valuation for the ....
....W VG be a set of vertices of G. Assume that the process Y starts in some state hs; pi 2 v, for some v 2 W . The set of behaviors of Y such that inf( p ) W has positive measure i W is a b.s.c. component of G. ut We discuss the diculty behind this lemma. In the discrete time model [7], where the system is given as a Markov chain and the speci cation as an automaton, the analogous lemma follows trivially from this property: if a vertex v is visited in nitely often by the process, then, each vertex v 0 , such that there is an edge vv 0 , is also visited in nitely often. ....
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C. Courcoubetis and M. Yannakakis. The complexity of probabilistic verication. Journal of the ACM, 42(4):857-907, 1995.
Model Checking - Clarke, Schlingloff (2000) (755 citations) (Correct)
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Courcoubetis C. and Yannakakis M. [1995], `The complexity of probabilistic veri cation', Journal of the ACM 42(4), 857-907.
On Probabilistic Computation Tree Logic - Ciesinski, Größer (2003) (1 citation) (Correct)
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Costas Courcoubetis and Mihalis Yannakakis. The complexity of probabilistic veri cation. Journal of the ACM, 42(4):857907, July 1995.
Verifying Qualitative Properties of - Probabilistic Programs Benedikt (Correct)
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Costas Courcoubetis and Mihalis Yannakakis. The complexity of probabilistic veri cation. Journal of the ACM, 42(4):857-907, July 1995.
Nash Equilibrium for Upward-Closed Objectives - Chatterjee (2005) (Correct)
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C. Courcoubetis and M. Yannakakis. The complexity of probabilistic veri cation. Journal of the ACM, 42(4):857-907, 1995. 26
Reachability Objectives - Krishnendu Chatterjee Luca (Correct)
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C. Courcoubetis and M. Yannakakis. The complexity of probabilistic veri cation. Journal of the ACM, 42(4):857-907, 1995.
Verifying Probabilistic Procedural Programs - Esparza, Etessami (2004) (1 citation) (Correct)
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C. Courcoubetis and M. Yannakakis. The complexity of probabilistic veri - cation. Journal of the ACM, 42(4):857-907, 1995.
Analysing Randomized Distributed Algorithms - Norman (Correct)
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C. Courcoubetis and M. Yannakakis. The complexity of probabilistic veri- cation. Journal of the ACM, 42(4):857-907, 1995.
Symbolic Model Checking of Probabilistic Processes .. - de Alfaro.. (2000) (5 citations) (Correct)
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C. Courcoubetis and M. Yannakakis. The complexity of probabilistic veri cation. Journal of the ACM, 42(4):857-907, 1995.
Implementation of Symbolic Model Checking for Probabilistic Systems - Parker (2002) (5 citations) (Correct)
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C. Courcoubetis and M. Yannakakis. The complexity of probabilistic veri - cation. Journal of the ACM, 42(4):857-907, 1995.
An Optimal Automata Approach to LTL Model . . . - Couvreur (2003) (Correct)
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Costas Courcoubetis and Mihalis Yannakakis. The complexity of probabilistic veri cation. Journal of the ACM, 42(4):857907, July 1995.
Symbolic Model Checking of Concurrent Probabilistic .. - Kwiatkowska.. (1999) (8 citations) (Correct)
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C. Courcoubetis and M. Yannakakis. The complexity of probabilistic veri cation. Journal of the ACM, 42(4):857-907, 1995.
On Almost Deterministic Timed Automata - Moura, Pinto (2001) (Correct)
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C. Courcoubetis and M. Yannakakis. The complexity of probabilistic veri cation. Journal of the ACM, 42(4):857-907, 1995.
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