## An Operational Semantics for Probabilistic Concurrent Constraint Programming (1998)

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Citations: | 30 - 12 self |

### BibTeX

@MISC{Pierro98anoperational,

author = {Alessandra Di Pierro and Herbert Wiklicky},

title = {An Operational Semantics for Probabilistic Concurrent Constraint Programming},

year = {1998}

}

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### Abstract

This paper investigates a probabilistic version of the concurrent constraint programming paradigm (CCP). The aim is to introduce the possibility to formulate so called "randomised algorithms" within the CCP framework. Differently from common approaches in (imperative) high-level programming languages, which rely on some kind of random() function, we introduce randomness in the very definition of the language by means of a probabilistic choice construct. This allows a program to make stochastic moves during its execution. We call the resulting language Probabilistic Concurrent Constraint Programming (PCCP). We present an operational semantics for PCCP by means of a probabilistic transition system such that the execution of a PCCP program may be seen as a stochastic process, i.e. as a random walk on the transition graph. The transition probabilities are given explicitly. This semantics captures a notion of observables which combines results of computations and the probability of those re...

### Citations

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Genetic Algorithms
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Citation Context ...oint of view. Various randomised algorithms and procedures have been investigated, of which we mention just a few examples: simulated annealing in combinatorial optimisation 1 [1], genetic algorithms =-=[5]-=-, probabilistic primality tests in particular for use in crypto-systems [19], and randomised proof procedures (e.g. for linear logic [15]). The benefits of randomisation at the base of the tremendous ... |

2257 |
Equations of state calculations by fast computing machines
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Citation Context ...hen will be executed) is one and the probability of an infinite loop is zero. Example 6.5 One of the most well known randomised algorithms is the so called Metropolis Algorithm or Simulated Annealing =-=[17, 1, 9]-=-. We will present this algorithm in the PCCP language and show how natural it fits into the framework of concurrent constraint programming. The strategy of this algorithm is inspired by the analogy wi... |

1289 | A Structured Approach to Operational Semantics
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Citation Context ...ecution. We define an operational semantics for PCCP by using the inductive style of Plotkin's SOS, i.e. by means of a transition system which describes the evolution of a program in a structural way =-=[20]-=-. Randomness is expressed by labels representing the probability that a transition takes place. Based on this we define a notion of observables which captures the (finite) results of computation toget... |

574 |
Approximation Algorithms for NP-Hard Problems
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Citation Context ...hen will be executed) is one and the probability of an infinite loop is zero. Example 6.5 One of the most well known randomised algorithms is the so called Metropolis Algorithm or Simulated Annealing =-=[17, 1, 9]-=-. We will present this algorithm in the PCCP language and show how natural it fits into the framework of concurrent constraint programming. The strategy of this algorithm is inspired by the analogy wi... |

436 | Concurrent Constraint Programming
- Saraswat, Rinard
- 1990
(Show Context)
Citation Context ...l CCP languages, PCCP is defined parametrically w.r.t. to a given constraint system. For PCCP we do not require any substantial modification of the standard cylindric constraint systems as defined in =-=[22, 23]-=-. In other words, we do not intend to introduce randomness on the data, which would require to restructure the constraint system as a fuzzy or belief system. Since the only randomisation is on the pro... |

378 |
Simulated Annealing and Boltzmann Machines
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Citation Context ...a complexity theoretic point of view. Various randomised algorithms and procedures have been investigated, of which we mention just a few examples: simulated annealing in combinatorial optimisation 1 =-=[1]-=-, genetic algorithms [5], probabilistic primality tests in particular for use in crypto-systems [19], and randomised proof procedures (e.g. for linear logic [15]). The benefits of randomisation at the... |

294 |
2001), Probability and Random Processes
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Citation Context ...aper we present a method of introducing a probabilistic nondeterminism in CCP. We explain the idea behind this notion by discussing an example well-known in probability theory, namely the random walk =-=[6, 7]-=-. 2.2 Random Walk In order to illustrate the difference between pure nondeterminism and our approach to a probabilistic version of nondeterminism consider a (directed or non-directed) graph \Gamma = (... |

252 | Semantic Foundations of Concurrent Constraint Programming
- Saraswat, Rinard, et al.
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Citation Context ...l CCP languages, PCCP is defined parametrically w.r.t. to a given constraint system. For PCCP we do not require any substantial modification of the standard cylindric constraint systems as defined in =-=[22, 23]-=-. In other words, we do not intend to introduce randomness on the data, which would require to restructure the constraint system as a fuzzy or belief system. Since the only randomisation is on the pro... |

170 |
Fuzzy Sets and Fuzzy Logic
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Citation Context ...of computation together with their probability of being computed. Since our intent is to randomise programs rather than data, we do not need to base our language on any kind of fuzzy or belief system =-=[12]-=-. Therefore, it is sufficient for our purpose to maintain the same standard (cylindric) constraint system as in CCP. The embedding of randomness within the semantics of a well structured programming p... |

136 |
Probabilistic Non-determinism
- Jones
- 1990
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Citation Context ...of random variables. Further work will lead to the formulation of a denotational semantics for PCCP. It is natural to base this semantics on measure theoretic notions, e.g. on spaces of measures, cf. =-=[21, 13, 11]-=-. We are already able to define a Banach space based semantics for a restricted version of PCCP in which all constraints in the probabilistic choice construct are true. We called this language Probabi... |

136 |
Semantics of probabilistic programs
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- 1981
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Citation Context ...ndomness is introduced either in an ad-hoc way by referring to some "external" function or procedure call (like random() in imperative languages such as C or FORTRAN), or by means of random =-=variables [13, 8]-=-. The resulting language, which we call Probabilistic CCP (PCCP), is then the concurrent constraint programming language where nondeterministic choice is replaced by a probabilistic one. This allows a... |

116 | Model checking for a probabilistic branching time logic with fairness
- Baier, Kwiatkowska
- 1998
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Citation Context ...itional investigations will also relate PCCP to other semantic approaches towards probabilistic computation, e.g. probabilistic predicate transformers [18, 16], probabilistic logic and model checking =-=[2, 10], and prob-=-abilistic process algebras [3]. A possible extension of the PCCP language can be obtained by considering a "fuzzy" constraint system where strict entailment is replaced by a weighted justifi... |

108 | Probabilistic predicate transformers
- Morgan, McIver, et al.
- 1996
(Show Context)
Citation Context ...he operational semantics given in this paper. Additional investigations will also relate PCCP to other semantic approaches towards probabilistic computation, e.g. probabilistic predicate transformers =-=[18, 16], probabil-=-istic logic and model checking [2, 10], and probabilistic process algebras [3]. A possible extension of the PCCP language can be obtained by considering a "fuzzy" constraint system where str... |

103 |
Introduction to Probability
- Grinstead, Snell
- 1997
(Show Context)
Citation Context ...aper we present a method of introducing a probabilistic nondeterminism in CCP. We explain the idea behind this notion by discussing an example well-known in probability theory, namely the random walk =-=[6, 7]-=-. 2.2 Random Walk In order to illustrate the difference between pure nondeterminism and our approach to a probabilistic version of nondeterminism consider a (directed or non-directed) graph \Gamma = (... |

96 | A tutorial on EMPA: A theory of concurrent processes with nondeterminism, priorities, probabilities and time. Theoretical Computer Science
- Bernardo, Gorrieri
- 1998
(Show Context)
Citation Context ... to other semantic approaches towards probabilistic computation, e.g. probabilistic predicate transformers [18, 16], probabilistic logic and model checking [2, 10], and probabilistic process algebras =-=[3]. A possib-=-le extension of the PCCP language can be obtained by considering a "fuzzy" constraint system where strict entailment is replaced by a weighted justification of constraints. This would be par... |

59 | D.: Stochastic Model Checking
- Kwiatkowska, Norman, et al.
- 2007
(Show Context)
Citation Context ...itional investigations will also relate PCCP to other semantic approaches towards probabilistic computation, e.g. probabilistic predicate transformers [18, 16], probabilistic logic and model checking =-=[2, 10], and prob-=-abilistic process algebras [3]. A possible extension of the PCCP language can be obtained by considering a "fuzzy" constraint system where strict entailment is replaced by a weighted justifi... |

22 |
CPO’s of measures for nondeterminism
- Saheb-Djahromi
- 1980
(Show Context)
Citation Context ...of random variables. Further work will lead to the formulation of a denotational semantics for PCCP. It is natural to base this semantics on measure theoretic notions, e.g. on spaces of measures, cf. =-=[21, 13, 11]-=-. We are already able to define a Banach space based semantics for a restricted version of PCCP in which all constraints in the probabilistic choice construct are true. We called this language Probabi... |

20 | Probabilistic concurrent constraint programming
- Gupta, Jagadeesan, et al.
- 1997
(Show Context)
Citation Context ...ndomness is introduced either in an ad-hoc way by referring to some "external" function or procedure call (like random() in imperative languages such as C or FORTRAN), or by means of random =-=variables [13, 8]-=-. The resulting language, which we call Probabilistic CCP (PCCP), is then the concurrent constraint programming language where nondeterministic choice is replaced by a probabilistic one. This allows a... |

13 |
Stochastic interaction and Linear Logic
- Lincoln, Mitchell, et al.
- 1995
(Show Context)
Citation Context ...nealing in combinatorial optimisation 1 [1], genetic algorithms [5], probabilistic primality tests in particular for use in crypto-systems [19], and randomised proof procedures (e.g. for linear logic =-=[15]-=-). The benefits of randomisation at the base of the tremendous growth of interest in such algorithms are simplicity and speed. For this reason the best known algorithms for many problems are nowaday r... |

11 | Probabilistic predicate transformers: Part 2
- McIver, Morgan
- 1996
(Show Context)
Citation Context ...he operational semantics given in this paper. Additional investigations will also relate PCCP to other semantic approaches towards probabilistic computation, e.g. probabilistic predicate transformers =-=[18, 16], probabil-=-istic logic and model checking [2, 10], and probabilistic process algebras [3]. A possible extension of the PCCP language can be obtained by considering a "fuzzy" constraint system where str... |

7 | Infinite Behaviour and Fairness in Concurrent Constraint Programming
- Kwiatkowska
- 1992
(Show Context)
Citation Context ...(x) in CCP (which is the same as the PCCP one but for the probability components of the guards) we obtain a more useful semantics. Since the nondeterminism occurring in the CCP formulation is angelic =-=[14] we are gu-=-aranteed that nat(x) generates all natural numbers. Note that in the CCP case "fairness" of the choice construct, i.e. all possible branches are sometime executed, is guaranteed by backtrack... |

6 | A Banach space based semantics for Probabilistic Concurrent Constraint Programming - Pierro, Wiklicky - 1998 |

5 | Implementing randomised algorithms in constraint logic programming - Angelopoulos, Pierro, et al. - 1998 |

3 |
Catuscia Palamidessi. Nondeterminism and infinite computations in constraint programming
- Boer, Pierro
- 1995
(Show Context)
Citation Context ...ration. The former is modelled as interleaving. As for the latter we use the notation 9 d x A for the agent A with local store d containing information on x which is hidden in the external store (see =-=[4, 22]-=- for further details). Obviously, the transition probability p is not changed by parallel composition and hiding. The execution of a procedure call, p(y), is modelled by the recursion rule R5 which re... |