Stochastic processes as concurrent constraint programs
Proceedings of the 26th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Quantitative solution of omega-regular games380872
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Games, Probability, and the Quantitative µ-Calculus qMµ
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Reduction and Refinement Strategies for Probabilistic Analysis
PAPM-PROBMIV '02 Proceedings of the Second Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Reachability Analysis of Probabilistic Systems by Successive Refinements
PAPM-PROBMIV '01 Proceedings of the Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Reduction and Refinement Strategies for Probabilistic Analysis
PAPM-PROBMIV '02 Proceedings of the Second Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Towards Quantitative Verification of Probabilistic Transition Systems
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Metrics for Labeled Markov Systems
CONCUR '99 Proceedings of the 10th International Conference on Concurrency Theory
Probabilistic Temporal Logics via the Modal Mu-Calculus
FoSSaCS '99 Proceedings of the Second International Conference on Foundations of Software Science and Computation Structure, Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS'99
Specifying Performance Measures for PEPA
ARTS '99 Proceedings of the 5th International AMAST Workshop on Formal Methods for Real-Time and Probabilistic Systems
Exploiting Modal Logic to Express Performance Measures
TOOLS '00 Proceedings of the 11th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools
Approximating labelled Markov processes
Information and Computation
Quantitative solution of omega-regular games
Journal of Computer and System Sciences - STOC 2001
Metrics for labelled Markov processes
Theoretical Computer Science - Logic, semantics and theory of programming
Model checking for a probabilistic branching time logic with fairness
Distributed Computing
A behavioural pseudometric for probabilistic transition systems
Theoretical Computer Science - Automata, languages and programming
Model checking discounted temporal properties
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2004)
On finite-state approximants for probabilistic computation tree logic
Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
Quantitative μ-calculus and CTL defined over constraint semirings
Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
A probabilistic polynomial-time process calculus for the analysis of cryptographic protocols
Theoretical Computer Science
Probabilistic temporal logics via the modal mu-calculus
Theoretical Computer Science
Results on the quantitative μ-calculus qMμ
ACM Transactions on Computational Logic (TOCL)
Reasoning about probabilistic sequential programs
Theoretical Computer Science
Distributed Extended Beam Search for Quantitative Model Checking
Model Checking and Artificial Intelligence
Quantitative μ-calculus and CTL Based on Constraint Semirings
Electronic Notes in Theoretical Computer Science (ENTCS)
A Novel Stochastic Game Via the Quantitative μ-calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
Reasoning About Imperative Quantum Programs
Electronic Notes in Theoretical Computer Science (ENTCS)
Characterising probabilistic processes logically
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Probabilistic modal µ-calculus with independent product
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Carrying probabilities to the infinite world
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
Reasoning about states of probabilistic sequential programs
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
On the decidability of temporal properties of probabilistic pushdown automata
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Verifying quantitative properties using bound functions
CHARME'05 Proceedings of the 13 IFIP WG 10.5 international conference on Correct Hardware Design and Verification Methods
Approximate Verification of the Symbolic Dynamics of Markov Chains
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
A proof system for compositional verification of probabilistic concurrent processes
FOSSACS'13 Proceedings of the 16th international conference on Foundations of Software Science and Computation Structures
Quantitative reactive modeling and verification
Computer Science - Research and Development
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Many notions of models in computer science provide quantitative information, or uncertainties, which necessitate a quantitative model checking paradigm. We present such a framework for reactive and generative systems based on a non-standard interpretation of the modal mu-calculus, where mu x.phi / nu x.phi are interpreted as least/greatest fixed points over the infinite lattice of maps from states to the unit interval. By letting formulas denote lower bounds of probabilistic evidence of properties, the values computed by our quantitative model checker can serve as satisfactory correctness guarantees in cases where conventional qualitative model checking fails. Since fixed point iteration in this infinite domain is computationally unfeasible, we establish that the computation of fixed points may be restated as a conventional, and on average efficient, optimization problem in linear programming; this holds for a fragment of the modal mu-calculus which subsumes CTL. Our semantics induces a state equivalence which is strictly in between probabilistic bisimulation and probabilistic ready bisimulation.