Algebraic laws for nondeterminism and concurrency
Journal of the ACM (JACM)
Communicating sequential processes
Communicating sequential processes
Observation equivalence as a testing equivalence
Theoretical Computer Science
Equivalences, congruences, and complete axiomatizations for probabilistic processes
CONCUR '90 Proceedings on Theories of concurrency : unification and extension: unification and extension
An efficient global convergence detection scheme for parallel algorithms on transputer networks
OUG-12 Proceedings of the 12th Occam User Group technical meeting on Tools and techniques for transputer applications
A synchronous calculus of relative frequency
CONCUR '90 Proceedings on Theories of concurrency : unification and extension: unification and extension
Bisimulation through probabilistic testing
Information and Computation
Elements of information theory
Elements of information theory
Technical Note: \cal Q-Learning
Machine Learning
Temporal difference learning and TD-Gammon
Communications of the ACM
Reactive, generative, and stratified models of probabilistic processes
Information and Computation
Bisimulation for probabilistic transition systems: a coalgebraic approach
Theoretical Computer Science
Testing preorders for probabilistic processes
Information and Computation
A Calculus of Communicating Systems
A Calculus of Communicating Systems
Introduction to Reinforcement Learning
Introduction to Reinforcement Learning
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
FORTE XII / PSTV XIX '99 Proceedings of the IFIP TC6 WG6.1 Joint International Conference on Formal Description Techniques for Distributed Systems and Communication Protocols (FORTE XII) and Protocol Specification, Testing and Verification (PSTV XIX)
Testing Equivalence for Processes
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Testing Labelled Markov Processes
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
The Linear Time - Branching Time Spectrum II
CONCUR '93 Proceedings of the 4th International Conference on Concurrency Theory
A Modal Characterisation of Observable Machine-Behaviour
CAAP '81 Proceedings of the 6th Colloquium on Trees in Algebra and Programming
Bisimulation for labelled Markov processes
Information and Computation - Special issue: LICS'97
Metrics for labelled Markov processes
Theoretical Computer Science - Logic, semantics and theory of programming
Bayesian sparse sampling for on-line reward optimization
ICML '05 Proceedings of the 22nd international conference on Machine learning
A testing scenario for probabilistic processes
Journal of the ACM (JACM)
Approximate Analysis of Probabilistic Processes: Logic, Simulation and Games
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
Representing systems with hidden state
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Learning the Difference between Partially Observable Dynamical Systems
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part II
Reinforcement learning: a survey
Journal of Artificial Intelligence Research
Planning and acting in partially observable stochastic domains
Artificial Intelligence
Bandit based monte-carlo planning
ECML'06 Proceedings of the 17th European conference on Machine Learning
Testing probabilistic equivalence through reinforcement learning
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Trace equivalence characterization through reinforcement learning
AI'06 Proceedings of the 19th international conference on Advances in Artificial Intelligence: Canadian Society for Computational Studies of Intelligence
Online testing with reinforcement learning
FATES'06/RV'06 Proceedings of the First combined international conference on Formal Approaches to Software Testing and Runtime Verification
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Checking if a given system implementation respects its specification is often done by proving that the two are ''equivalent''. The equivalence is chosen, in particular, for its computability and of course for its meaning, that is, for its adequacy with what is observable from the two systems (implementation and specification). Trace equivalence is easily testable (decidable from interaction), but often considered too weak; in contrast, bisimulation is accepted as the canonical equivalence for interaction, but it is not testable. Richer than an equivalence is a form of distance: it is zero between equivalent systems, and it provides an estimation of their difference if the systems are not equivalent. Our main contribution is to define such a distance in a context where (1) the two systems to be compared have a stochastic behavior; (2) the model of one of them (e.g., the implementation) is unknown, hence our only knowledge is obtained by interacting with it; (3) consequently the target equivalence (observed when distance is zero) must be testable. To overcome the problem that the model is unknown, we use a Reinforcement Learning approach that provides powerful stochastic algorithms that only need to interact with the model. Our second main contribution is a new family of testable equivalences, called K-moment. The weakest of them, 1-moment equivalence, is trace equivalence; as K grows, K-moment equivalences become finer, all remaining, as well as their limit, weaker than bisimulation. We propose a framework to define (and test) a bigger class of testable equivalences: Test-Observation-Equivalences (TOEs), and we show how they can be made coarser or not, by tuning some parameters.