Citation
Krishnendu Chatterjee, Tom Henzinger, Koushik Sen. "Model-Checking omega-Regular Properties of Interval Markov Chains". Foundations of Software Science and Computation Structure (FoSSaCS) 2008, Roberto M. Amadio (ed.), 302-317, March, 2008.

Abstract
We study the problem of model checking Interval-valued Discrete-time Markov Chains (IDTMC). IDTMCs are discrete-time finite Markov Chains for which the exact transition probabilities are not known. Instead in IDTMCs, each transition is associated with an interval in which the actual transition probability must lie. We consider two semantic interpretations for the uncertainty in the transition probabilities of an IDTMC. In the first interpretation, we think of an IDTMC as representing a (possibly uncountable) family of (classical) discrete-time Markov Chains, where each member of the family is a Markov Chain whose transition probabilities lie within the interval range given in the IDTMC. We call this semantic interpretation Uncertain Markov Chains (UMC). In the second semantics for an IDTMC, which we call Interval Markov Decision Process (IMDP), we view the uncertainty as being resolved through non-determinism. In other words, each time a state is visited, we adversarially pick a transition distribution that respects the interval constraints, and take a probabilistic step according to the chosen distribution. We introduce a logic omega-PCTL that can express liveness, strong fairness, and omega-regular properties (such properties cannot be expressed in PCTL). We show that the omega-PCTL model checking problem for Uncertain Markov Chain semantics is decidable in PSPACE (same as the best known upper bound for PCTL) and for Interval Markov Decision Process semantics is decidable in coNP (improving the previous known PSPACE bound for PCTL). We also show that the qualitative fragment of the logic can be solved in coNP for the UMC interpretation, and can be solved in polynomial time for a sub-class of UMCs. We also prove lower bounds for these model checking problems.We show that the model checking problem of IDTMCs with LTL formulas can be solved for both UMC and IMDP semantics by reduction to the model checking problem of IDTMC with omega-PCTL formulas.

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• http://dx.doi.org/10.1007/978-3-540-78499-9_22

• HTML

  Krishnendu Chatterjee, Tom Henzinger, Koushik Sen. <a
  href="http://chess.eecs.berkeley.edu/pubs/469.html"
  >Model-Checking omega-Regular Properties of Interval
  Markov Chains</a>, Foundations of Software Science and
  Computation Structure (FoSSaCS) 2008, Roberto M. Amadio
  (ed.), 302-317, March, 2008.

• Plain text

  Krishnendu Chatterjee, Tom Henzinger, Koushik Sen.
  "Model-Checking omega-Regular Properties of Interval
  Markov Chains". Foundations of Software Science and
  Computation Structure (FoSSaCS) 2008, Roberto M. Amadio
  (ed.), 302-317, March, 2008.

• BibTeX

  @inproceedings{ChatterjeeHenzingerSen08_ModelCheckingOmegaRegularPropertiesOfIntervalMarkov,
      author = {Krishnendu Chatterjee and Tom Henzinger and
                Koushik Sen},
      title = {Model-Checking omega-Regular Properties of
                Interval Markov Chains},
      booktitle = {Foundations of Software Science and Computation
                Structure (FoSSaCS) 2008},
      editor = {Roberto M. Amadio},
      pages = {302-317},
      month = {March},
      year = {2008},
      abstract = {We study the problem of model checking
                Interval-valued Discrete-time Markov Chains
                (IDTMC). IDTMCs are discrete-time finite Markov
                Chains for which the exact transition
                probabilities are not known. Instead in IDTMCs,
                each transition is associated with an interval in
                which the actual transition probability must lie.
                We consider two semantic interpretations for the
                uncertainty in the transition probabilities of an
                IDTMC. In the first interpretation, we think of an
                IDTMC as representing a (possibly uncountable)
                family of (classical) discrete-time Markov Chains,
                where each member of the family is a Markov Chain
                whose transition probabilities lie within the
                interval range given in the IDTMC. We call this
                semantic interpretation Uncertain Markov Chains
                (UMC). In the second semantics for an IDTMC, which
                we call Interval Markov Decision Process (IMDP),
                we view the uncertainty as being resolved through
                non-determinism. In other words, each time a state
                is visited, we adversarially pick a transition
                distribution that respects the interval
                constraints, and take a probabilistic step
                according to the chosen distribution. We introduce
                a logic omega-PCTL that can express liveness,
                strong fairness, and omega-regular properties
                (such properties cannot be expressed in PCTL). We
                show that the omega-PCTL model checking problem
                for Uncertain Markov Chain semantics is decidable
                in PSPACE (same as the best known upper bound for
                PCTL) and for Interval Markov Decision Process
                semantics is decidable in coNP (improving the
                previous known PSPACE bound for PCTL). We also
                show that the qualitative fragment of the logic
                can be solved in coNP for the UMC interpretation,
                and can be solved in polynomial time for a
                sub-class of UMCs. We also prove lower bounds for
                these model checking problems.We show that the
                model checking problem of IDTMCs with LTL formulas
                can be solved for both UMC and IMDP semantics by
                reduction to the model checking problem of IDTMC
                with omega-PCTL formulas.},
      URL = {http://chess.eecs.berkeley.edu/pubs/469.html}
  }
  

Posted by Krishnendu Chatterjee, PhD on 24 Jun 2008.
Groups: chess
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