Characterizing finite Kripke structures in propositional temporal logic
Theoretical Computer Science - International Joint Conference on Theory and Practice of Software Development, P
POPL '88 Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A hierarchy of temporal properties (invited paper, 1989)
PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
Operational and algebraic semantics of concurrent processes
Handbook of theoretical computer science (vol. B)
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
The temporal logic of reactive and concurrent systems
The temporal logic of reactive and concurrent systems
Modeling and verification of randomized distributed real-time systems
Modeling and verification of randomized distributed real-time systems
Competitive Markov decision processes
Competitive Markov decision processes
ACM Transactions on Programming Languages and Systems (TOPLAS)
Quantitative solution of omega-regular games380872
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Finite State Markovian Decision Processes
Finite State Markovian Decision Processes
Alternating-time temporal logic
Journal of the ACM (JACM)
The Metric Analogue of Weak Bisimulation for Probabilistic Processes
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
CONCUR '98 Proceedings of the 9th International Conference on Concurrency Theory
Equivalences, Congruences, and Complete Axiomatizations for Probabilistic Processes
CONCUR '90 Proceedings of the Theories of Concurrency: Unification and Extension
Probabilistic Simulations for Probabilistic Processes
CONCUR '94 Proceedings of the Concurrency Theory
On Model-Checking for Fragments of µ-Calculus
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
Alternating Refinement Relations
CONCUR '98 Proceedings of the 9th International Conference on Concurrency Theory
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Automatic verification of probabilistic concurrent finite state programs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
A behavioural pseudometric for metric labelled transition systems
CONCUR 2005 - Concurrency Theory
Games where you can play optimally without any memory
CONCUR 2005 - Concurrency Theory
Model checking discounted temporal properties
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2004)
Approximating and computing behavioural distances in probabilistic transition systems
Theoretical Computer Science
Skew and infinitary formal power series
Theoretical Computer Science
Characterize branching distance in terms of (η,α)-bisimilarity
Information and Computation
25 Years of Model Checking
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Discounted Properties of Probabilistic Pushdown Automata
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Better Quality in Synthesis through Quantitative Objectives
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Approximating a behavioural pseudometric without discount for probabilistic systems
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Quantitative generalizations of languages
DLT'07 Proceedings of the 11th international conference on Developments in language theory
Recognizable tree series with discounting
Acta Cybernetica
Weighted automata and weighted logics with discounting
CIAA'07 Proceedings of the 12th international conference on Implementation and application of automata
ACM Transactions on Computational Logic (TOCL)
Time for verification
CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
On memoryless quantitative objectives
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Timed automata can always be made implementable
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
Theoretical Computer Science
Deterministic priority mean-payoff games as limits of discounted games
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Quantifying similarities between timed systems
FORMATS'05 Proceedings of the Third international conference on Formal Modeling and Analysis of Timed Systems
An accessible approach to behavioural pseudometrics
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
A survey of stochastic ω-regular games
Journal of Computer and System Sciences
Quantitative µ-calculus analysis of power management in wireless networks
ICTAC'06 Proceedings of the Third international conference on Theoretical Aspects of Computing
Measuring and synthesizing systems in probabilistic environments
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Equational weighted tree transformations with discounting
Algebraic Foundations in Computer Science
Robustness of structurally equivalent concurrent parity games
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
Giving advice to people in path selection problems
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Computing game metrics on markov decision processes
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
A pseudometric in supervisory control of probabilistic discrete event systems
Discrete Event Dynamic Systems
Perfect information stochastic priority games
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
Towards communication-based steering of complex distributed systems
Proceedings of the 17th Monterey conference on Large-Scale Complex IT Systems: development, operation and management
Weighted modal transition systems
Formal Methods in System Design
Quantitative reactive modeling and verification
Computer Science - Research and Development
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Discounting the future means that the value, today, of a unit payoffis 1 if the payoff occurs today, a if it occurs tomorrow, a2 if it occurs the day after tomorrow, and so on, for some real-valued discount factor 0 ≤ a ≤ 1. Discounting (or inflation) is a key paradigm in economics and has been studied in Markov decision processes as well as game theory. We submit that discounting also has a natural place in systems engineering: for nonterminating systems, a potential bug in the faraway future is less troubling than a potential bug today. We therefore develop a systems theory with discounting. Our theory includes several basic elements: discounted versions of system properties that correspond to the ω-regular properties, fixpoint-based algorithms for checking discounted properties, and a quantitative notion of bisimilarity for capturing the difference between two states with respect to discounted properties. We present the theory in a general form that applies to probabilistic systems as well as multicomponent systems (games), but it readily specializes to classical transition systems. We show that discounting, besides its natural practical appeal, has also several mathematical benefits. First, the resulting theory is robust, in that small perturbations of a system can cause only small changes in the properties of the system. Second, the theory is computational, in that the values of discounted properties, as well as the discounted bisimilarity distance between states, can be computed to any desired degree of precision.