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417
Universal coalgebra: a theory of systems
, 2000
"... In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certa ..."
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Cited by 302 (32 self)
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In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certain types of automata and more generally, for (transition and dynamical) systems. An important property of initial algebras is that they satisfy the familiar principle of induction. Such a principle was missing for coalgebras until the work of Aczel (NonWellFounded sets, CSLI Leethre Notes, Vol. 14, center for the study of Languages and information, Stanford, 1988) on a theory of nonwellfounded sets, in which he introduced a proof principle nowadays called coinduction. It was formulated in terms of bisimulation, a notion originally stemming from the world of concurrent programming languages. Using the notion of coalgebra homomorphism, the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras. Thus, the three basic notions of universal algebra: algebra, homomorphism of algebras, and congruence, turn out to correspond to coalgebra, homomorphism of coalgebras, and bisimulation, respectively. In this paper, the latter are taken
Probabilistic Simulations for Probabilistic Processes
, 1994
"... Several probabilistic simulation relations for probabilistic systems are defined and evaluated according to two criteria: compositionality and preservation of "interesting" properties. Here, the interesting properties of a system are identified with those that are expressible in an untimed ..."
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Cited by 275 (18 self)
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Several probabilistic simulation relations for probabilistic systems are defined and evaluated according to two criteria: compositionality and preservation of "interesting" properties. Here, the interesting properties of a system are identified with those that are expressible in an untimed version of the Timed Probabilistic concurrent Computation Tree Logic (TPCTL) of Hansson. The definitions are made, and the evaluations carried out, in terms of a general labeled transition system model for concurrent probabilistic computation. The results cover weak simulations, which abstract from internal computation, as well as strong simulations, which do not.
Relations in Concurrency
"... The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the seman ..."
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Cited by 263 (33 self)
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The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the semantics of nondeterministic dataflow. Profunctors are shown to play a key role in relating models for concurrency and to support an interpretation as higherorder processes (where input and output may be processes). Two recent directions of research are described. One is concerned with a language and computational interpretation for profunctors. This addresses the duality between input and output in profunctors. The other is to investigate general spans of event structures (the spans can be viewed as special profunctors) to give causal semantics to higherorder processes. For this it is useful to generalise event structures to allow events which “persist.”
Reactive, Generative and Stratified Models of Probabilistic Processes
 Information and Computation
, 1990
"... ion Let E; E 0 be PCCS expressions. The intermodel abstraction rule IMARGR is defined by E ff[p] \Gamma\Gamma! i E 0 =) E ff[p= G (E;fffg)] ae \Gamma\Gamma\Gamma\Gamma\Gamma\Gamma! i E 0 This rule uses the generative normalization function to convert generative probabilities to reactive ..."
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Cited by 155 (6 self)
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ion Let E; E 0 be PCCS expressions. The intermodel abstraction rule IMARGR is defined by E ff[p] \Gamma\Gamma! i E 0 =) E ff[p= G (E;fffg)] ae \Gamma\Gamma\Gamma\Gamma\Gamma\Gamma! i E 0 This rule uses the generative normalization function to convert generative probabilities to reactive ones, thereby abstracting away from the relative probabilities between different actions. We can now define 'GR ('G (P )) as the reactive transition system that can be inferred from P 's generative transition system via IMARGR . By the same procedure as described at the end of Section 3.1, 'GR can be extended to a mapping 'GR : j GG ! j GR . Write P GR ¸ Q if P; Q 2 Pr are reactive bisimulation equivalent with respect to the transitions derivable from G+IMARGR , i.e. the theory obtained by adding IMARGR to the rules of Figure 7. The equivalence GR ¸ is defined just like R ¸ but using the cPDF ¯GR instead of ¯R . ¯GR is defined by ¯GR (P; ff; S) = X i2I R (=I G ) fj p i j G+ I...
Modelchecking algorithms for continuoustime Markov chains
 IEEE TRANSACTIONS ON SOFTWARE ENGINEERING
, 2003
"... Continuoustime Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steadystate and transientstate probabilities. This paper introduces a branching temporal logic for expressing realt ..."
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Cited by 139 (25 self)
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Continuoustime Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steadystate and transientstate probabilities. This paper introduces a branching temporal logic for expressing realtime probabilistic properties on CTMCs and presents approximate model checking algorithms for this logic. The logic, an extension of the continuous stochastic logic CSL of Aziz et al., contains a timebounded until operator to express probabilistic timing properties over paths as well as an operator to express steadystate probabilities. We show that the model checking problem for this logic reduces to a system of linear equations (for unbounded until and the steadystate operator) and a Volterra integral equation system (for timebounded until). We then show that the problem of modelchecking timebounded until properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows the verification of probabilistic timing properties by efficient techniques for transient analysis for CTMCs such as uniformization. Finally, we show that a variant of lumping equivalence (bisimulation), a wellknown notion for aggregating CTMCs, preserves the validity of all formulas in the logic.
Probabilistic noninterference for multithreaded programs
 In Proc. IEEE Computer Sec. Foundations Workshop
, 2000
"... ..."
Model Checking for a Probabilistic Branching Time Logic with Fairness
 Distributed Computing
, 1998
"... We consider concurrent probabilistic systems, based on probabilistic automata of Segala & Lynch [55], which allow nondeterministic choice between probability distributions. These systems can be decomposed into a collection of "computation trees" which arise by resolving the nondeterm ..."
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Cited by 116 (35 self)
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We consider concurrent probabilistic systems, based on probabilistic automata of Segala & Lynch [55], which allow nondeterministic choice between probability distributions. These systems can be decomposed into a collection of "computation trees" which arise by resolving the nondeterministic, but not probabilistic, choices. The presence of nondeterminism means that certain liveness properties cannot be established unless fairness is assumed. We introduce a probabilistic branching time logic PBTL, based on the logic TPCTL of Hansson [30] and the logic PCTL of [55], resp. pCTL of [14]. The formulas of the logic express properties such as "every request is eventually granted with probability at least p". We give three interpretations for PBTL on concurrent probabilistic processes: the first is standard, while in the remaining two interpretations the branching time quantifiers are taken to range over a certain kind of fair computation trees. We then present a model checking algorithm for...
Priorities in process algebra
, 1999
"... This chapter surveys the semantic rami cations of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. The need for these enriched formalisms arises when one wishes to model system features such asinterrupts, prioritized ..."
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Cited by 102 (11 self)
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This chapter surveys the semantic rami cations of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. The need for these enriched formalisms arises when one wishes to model system features such asinterrupts, prioritized choice, orrealtime behavior. Approaches to priority in process algebras can be classi ed according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global preemption and static priorities and led to formalisms for modeling interrupts and aspects of realtime, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of preemption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the e cient encoding of realtime semantics. Technically, this chapter studies the di erent models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local preemption. In each case the operational semantics of CCS is modi ed appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for di erent processalgebraic settings are discussed.
A tutorial on EMPA: A theory of concurrent processes with nondeterminism, priorities, probabilities and time
 Theoretical Computer Science
, 1998
"... In this tutorial we give an overview of the process algebra EMPA, a calculus devised in order to model and analyze features of realworld concurrent systems such as nondeterminism, priorities, probabilities and time, with a particular emphasis on performance evaluation. The purpose of this tutorial ..."
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Cited by 96 (9 self)
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In this tutorial we give an overview of the process algebra EMPA, a calculus devised in order to model and analyze features of realworld concurrent systems such as nondeterminism, priorities, probabilities and time, with a particular emphasis on performance evaluation. The purpose of this tutorial is to explain the design choices behind the development of EMPA and how the four features above interact, and to show that a reasonable trade off between the expressive power of the calculus and the complexity of its underlying theory has been achieved.
Equivalence notions and model minimization in Markov decision processes
, 2003
"... Many stochastic planning problems can be represented using Markov Decision Processes (MDPs). A difficulty with using these MDP representations is that the common algorithms for solving them run in time polynomial in the size of the state space, where this size is extremely large for most realworld ..."
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Cited by 95 (2 self)
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Many stochastic planning problems can be represented using Markov Decision Processes (MDPs). A difficulty with using these MDP representations is that the common algorithms for solving them run in time polynomial in the size of the state space, where this size is extremely large for most realworld planning problems of interest. Recent AI research has addressed this problem by representing the MDP in a factored form. Factored MDPs, however, are not amenable to traditional solution methods that call for an explicit enumeration of the state space. One familiar way to solve MDP problems with very large state spaces is to form a reduced (or aggregated) MDP with the same properties as the original MDP by combining “equivalent ” states. In this paper, we discuss applying this approach to solving factored MDP problems—we avoid enumerating the state space by describing large blocks of “equivalent” states in factored form, with the block descriptions being inferred directly from the original factored representation. The resulting reduced MDP may have exponentially fewer states than the original factored MDP, and can then be solved using traditional methods. The reduced MDP found depends on the notion of equivalence between states used in the aggregation. The notion of equivalence chosen will be fundamental in designing and analyzing