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16
Probabilistic Automata: System Types, Parallel Composition and Comparison
 In Validation of Stochastic Systems: A Guide to Current Research
, 2004
"... We survey various notions of probabilistic automata and probabilistic bisimulation, accumulating in an expressiveness hierarchy of probabilistic system types. The aim of this paper is twofold: On the one hand it provides an overview of existing types of probabilistic systems and, on the other ha ..."
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Cited by 35 (5 self)
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We survey various notions of probabilistic automata and probabilistic bisimulation, accumulating in an expressiveness hierarchy of probabilistic system types. The aim of this paper is twofold: On the one hand it provides an overview of existing types of probabilistic systems and, on the other hand, it explains the relationship between these models.
A.: Timed I/O Automata: A Complete Specification Theory for Realtime Systems
 In: HSCC 2010
, 2010
"... A specification theory combines notions of specifications and implementations with a satisfaction relation, a refinement relation and a set of operators supporting stepwise design. We develop a complete specification framework for realtime systems using Timed I/O Automata as the specification form ..."
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Cited by 34 (15 self)
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A specification theory combines notions of specifications and implementations with a satisfaction relation, a refinement relation and a set of operators supporting stepwise design. We develop a complete specification framework for realtime systems using Timed I/O Automata as the specification formalism, with the semantics expressed in terms of Timed I/O Transition Systems. We provide constructs for refinement, consistency checking, logical and structural composition, and quotient of specifications – all indispensable ingredients of a compositional design methodology. The theory is implemented on top of an engine for timed games, Uppaaltiga, and illustrated with a small case study.
Describing and executing random reactive systems
 In SEFM 2006, 4th IEEE International Conference on Software Engineering and Formal Methods
, 2006
"... We propose a operational model for describing nondeterministic reactive systems, together with a mechanism for expressing probability issues. Some models have already been proposed for this purposes, but they are generally intended to allow global reasoning on systems (e.g. stockastic analysis, form ..."
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Cited by 10 (8 self)
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We propose a operational model for describing nondeterministic reactive systems, together with a mechanism for expressing probability issues. Some models have already been proposed for this purposes, but they are generally intended to allow global reasoning on systems (e.g. stockastic analysis, formal proofs). Our goal is somehow less ambitious, sinve we are mainly interested in executing such models, which can be useful for testing, prototyping. On the other hand, the proposed model is not strongly restricted because of decidability concerns, so it is likely to be more expressive: in particular, we are not restricted to finitestate models. The proposed model is rather general: systems are described as implicit state/transition machines, possibly infinite, where probabilities are expressed by means of relative weights. The model itself is more an abstract machine than a programming language. The idea is then to propose highlevel, userfriendly languages that can be compiled into the model. We present such a language, based on regular expressions, together with its translation into the model. 1
A Survey of Markovian Behavioral Equivalences
"... Abstract. Markovian behavioral equivalences are a means to relate and manipulate the formal descriptions of systems with an underlying CTMC semantics. There are three fundamental approaches to their definition: bisimilarity, testing, and trace. In this paper we survey the major results appeared in t ..."
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Cited by 8 (1 self)
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Abstract. Markovian behavioral equivalences are a means to relate and manipulate the formal descriptions of systems with an underlying CTMC semantics. There are three fundamental approaches to their definition: bisimilarity, testing, and trace. In this paper we survey the major results appeared in the literature about Markovian bisimilarity, Markovian testing equivalence, and Markovian trace equivalence. The objective is to compare these equivalences with respect to a number of criteria such as their discriminating power, the exactness of the CTMClevel aggregations they induce, the achievement of the congruence property, the existence of sound and complete axiomatizations, the existence of logical characterizations, and the existence of efficient verification algorithms. 1
On the verification of probabilistic I/O automata with unspecified rates
 In SAC ’09: Proceedings of the 2009 ACM symposium on Applied Computing
, 2009
"... We consider the Probabilistic I/O Automata framework, for which we address the verification of reachability properties in case the rates (also called delay parameters) are unspecified. We show that the problem of finding (or even approximating) the supremum probability that a set of states is reac ..."
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Cited by 7 (7 self)
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We consider the Probabilistic I/O Automata framework, for which we address the verification of reachability properties in case the rates (also called delay parameters) are unspecified. We show that the problem of finding (or even approximating) the supremum probability that a set of states is reached is undecidable. However, we give an algorithm to obtain a nontrivial overestimation of this value. We explain why this overestimation may result useful for many systems. Finally, in order to compare our approach against Markov Decision Processes, we study a simple protocol for anonymous fair service. In this case, the overestimation computed over the PIOA gives a more realistic result than the exact computation over the MDP.
Probabilistic timed I/O automata with continuous state spaces. Preliminary version available at http://theory.lcs.mit.edu/˜mitras/research/ csptioa_preprint.pdf
, 2006
"... Abstract. We present Piecewise Deterministic Timed I/O Automata (PDTIOA): a new continuous state automaton model that allows both nondeterministic and probabilistic discrete transitions, along with continuous deterministic trajectories. We use a partition of actions, called tasks and a task schedule ..."
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Cited by 3 (3 self)
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Abstract. We present Piecewise Deterministic Timed I/O Automata (PDTIOA): a new continuous state automaton model that allows both nondeterministic and probabilistic discrete transitions, along with continuous deterministic trajectories. We use a partition of actions, called tasks and a task scheduler to resolve nondeterministic choice over actions. We define a topology on the set of trajectories and make a key continuity assumption about maximal length of trajectories. Together, these structures enable us to construct a natural probability measure over the space of executions and the space of traces. The resulting PDTIOA framework yields simple notions of external behavior and implementation, and has simple compositionality properties. By introducing local schedulers, we generalize PDTIOAs to allow nondeterministic trajectories and stopping times. 1
Markovian testing and trace equivalences exactly lump more than Markovian bisimilarity
 International Workshop on Algebraic Process Calculi: The First Twenty Five Years and Beyond (APC 25), Electronic Notes in Theoretical Computer Science
, 2005
"... The notion of equivalence that is typically used to relate Markovian process terms and to reduce their underlying state spaces is Markovian bisimilarity. The reason is that, besides being a congruence, Markovian bisimilarity is consistent with ordinary lumping, an exact aggregation for Markov chains ..."
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Cited by 3 (2 self)
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The notion of equivalence that is typically used to relate Markovian process terms and to reduce their underlying state spaces is Markovian bisimilarity. The reason is that, besides being a congruence, Markovian bisimilarity is consistent with ordinary lumping, an exact aggregation for Markov chains. In this paper we show that two nonbisimulationbased Markovian behavioral equivalences – Markovian testing equivalence and Markovian trace equivalence – induce at the Markov chain level an aggregation strictly coarser than ordinary lumping that is still exact. 1
On the Expressiveness of Markovian Process Calculi with Durational and Durationless Actions
"... Several Markovian process calculi have been proposed in the literature, which differ from each other for various aspects. With regard to the action representation, we distinguish between integratedtime Markovian process calculi, in which every action has an exponentially distributed duration associ ..."
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Cited by 2 (2 self)
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Several Markovian process calculi have been proposed in the literature, which differ from each other for various aspects. With regard to the action representation, we distinguish between integratedtime Markovian process calculi, in which every action has an exponentially distributed duration associated with it, and orthogonaltime Markovian process calculi, in which action execution is separated from time passing. Similar to deterministically timed process calculi, we show that these two options are not irreconcilable by exhibiting three mappings from an integratedtime Markovian process calculus to an orthogonaltime Markovian process calculus that preserve the behavioral equivalence of process terms under different interpretations of action execution: eagerness, laziness, and maximal progress. The mappings are limited to classes of process terms of the integratedtime Markovian process calculus with restrictions on parallel composition and do not involve the full capability of the orthogonaltime Markovian process calculus of expressing nondeterministic choices, thus elucidating the only two important differences between the two calculi: their synchronization disciplines and their ways of solving choices. 1
Tracebased Semantics for Probabilistic Timed I/O Automata Submitted for review. Full version http://theory.lcs.mit.edu/ ∼mitras/ research/PTIOA06full.pdf
"... Abstract. We propose the Probabilistic Timed I/O Automaton (PTIOA) framework for modelling and analyzing discretely communicating probabilistic hybrid systems. State transition of a PTIOA can be nondeterministic or probabilistic. Probabilistic choices can be based on continuous distributions. Contin ..."
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Abstract. We propose the Probabilistic Timed I/O Automaton (PTIOA) framework for modelling and analyzing discretely communicating probabilistic hybrid systems. State transition of a PTIOA can be nondeterministic or probabilistic. Probabilistic choices can be based on continuous distributions. Continuous evolution of a PTIOA is purely nondeterministic. PTIOAs can communicate through shared actions. By supporting external nondeterminism, the framework allows us to model arbitrary interleaving of concurrently executing automata. The framework generalizes several previously studied automata models of its class. We develop the tracebased semantics for PTIOAs which involves measure theoretic constructions on the space of executions of the automata. We introduce a new notion of external behavior for PTIOAs and show that PTIOAs have simple compositionality properties with respect this external behavior. 1
Probabilistic I/O Automata: Theories of Two Equivalences
, 2006
"... Working in the context of a processalgebraic language for Probabilistic I/O Automata (PIOA), we study the notion of PIOA behavior equivalence by obtaining a complete axiomatization of its equational theory and comparing the results with a complete axiomatization of a more standard equivalence, weig ..."
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Cited by 1 (0 self)
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Working in the context of a processalgebraic language for Probabilistic I/O Automata (PIOA), we study the notion of PIOA behavior equivalence by obtaining a complete axiomatization of its equational theory and comparing the results with a complete axiomatization of a more standard equivalence, weighted bisimulation. The axiomatization of behavior equivalence is achieved by adding to the language an operator for forming convex combinations of terms.