An analysis of stochastic shortest path problems
Mathematics of Operations Research
The complexity of probabilistic verification
Journal of the ACM (JACM)
State-space support for path-based reward variables
IPDS '98 Proceedings of the third IEEE international performance and dependability symposium on International performance and dependability symposium
Model checking
Passage time distributions in large Markov chains
SIGMETRICS '02 Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
On the Logical Characterisation of Performability Properties
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Temporal Logics for the Specification of Performance and Reliability
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Modeling Using Stochastic Reward Nets
MASCOTS '93 Proceedings of the International Workshop on Modeling, Analysis, and Simulation On Computer and Telecommunication Systems
Computing Minimum and Maximum Reachability Times in Probabilistic Systems
CONCUR '99 Proceedings of the 10th International Conference on Concurrency Theory
It Usually Works: The Temporal Logic of Stochastic Systems
Proceedings of the 7th International Conference on Computer Aided Verification
Specifying Performance Measures for PEPA
ARTS '99 Proceedings of the 5th International AMAST Workshop on Formal Methods for Real-Time and Probabilistic Systems
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Implicit GSPN reachability set generation using decision diagrams
Performance Evaluation - Dependable systems and networks-performance and dependability symposium (DSN-PDS) 2002: Selected papers
Model checking discounted temporal properties
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2004)
Model Checking Markov Chains with Actions and State Labels
IEEE Transactions on Software Engineering
Quantitative verification: models techniques and tools
Proceedings of the the 6th joint meeting of the European software engineering conference and the ACM SIGSOFT symposium on The foundations of software engineering
CSL^TA: an Expressive Logic for Continuous-Time Markov Chains
QEST '07 Proceedings of the Fourth International Conference on Quantitative Evaluation of Systems
Performance Trees: Expressiveness and Quantitative Semantics
QEST '07 Proceedings of the Fourth International Conference on Quantitative Evaluation of Systems
PRISM: probabilistic model checking for performance and reliability analysis
ACM SIGMETRICS Performance Evaluation Review
Model checking durational probabilistic systems
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
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There are currently a variety of logics used to describe properties of discrete-state systems, such as linear temporal logic (LTL) and computation tree logic (CTL), and of discrete-state stochastic systems, such as probabilistic CTL (PCTL) and continuous stochastic logic (CSL). While powerful, these logics are by definition limited to producing only true or false responses. In this work, we introduce a query language, CTML, that operates on real-valued quantities to reason over probabilistic systems. CTML is inspired by, and evolves from stochastic logic. It extends until and weak until with arithmetic operations on real values, while still preserving their conventional semantics of temporal logic. We derive mathematical algorithms for computing each of the operators, show how any PCTL property can be expressed in CTML, and illustrate the expressiveness of CTML with some example performance-related queries.