## Structural Operational Semantics for Stochastic Process Calculi

Citations: | 11 - 0 self |

### BibTeX

@MISC{Klin_structuraloperational,

author = {Bartek Klin and Vladimiro Sassone},

title = {Structural Operational Semantics for Stochastic Process Calculi},

year = {}

}

### OpenURL

### Abstract

Abstract. A syntactic framework called SGSOS, for defining well-behaved Markovian stochastic transition systems, is introduced by analogy to the GSOS congruence format for nondeterministic processes. Stochastic bisimilarity is guaranteed a congruence for systems defined by SGSOS rules. Associativity of parallel composition in stochastic process algebras is also studied within the framework. 1

### Citations

3682 | Communicating Sequential Processes
- Hoare
- 1978
(Show Context)
Citation Context ... for systems defined by SGSOS rules. Associativity of parallel composition in stochastic process algebras is also studied within the framework. 1 Introduction Process algebras such as CCS [18] or CSP =-=[5]-=- are widely accepted as useful tools for compositional modeling of nondeterministic, communicating processes. Their semantics is usually described within the framework of Structural Operational Semant... |

1434 |
A Calculus of Communicating Systems
- Milner
- 1980
(Show Context)
Citation Context ...a congruence for systems defined by SGSOS rules. Associativity of parallel composition in stochastic process algebras is also studied within the framework. 1 Introduction Process algebras such as CCS =-=[18]-=- or CSP [5] are widely accepted as useful tools for compositional modeling of nondeterministic, communicating processes. Their semantics is usually described within the framework of Structural Operati... |

1385 | A structural approach to operational semantics
- Plotkin
- 2004
(Show Context)
Citation Context ...y accepted as useful tools for compositional modeling of nondeterministic, communicating processes. Their semantics is usually described within the framework of Structural Operational Semantics (SOS) =-=[19]-=-, where labelled nondeterministic transition systems (LTSs) are defined by induction on the syntactic structure of processes. Formalisms for SOS decriptions of nondeterministic systems have been widel... |

648 | A Compositional Approach to Performance Modelling
- Hillston
- 1994
(Show Context)
Citation Context ...ovided that it makes some a-transition. 3sVarious equivalence relations on states in RTSs have been considered. Of those, the most significant is stochastic bisimilarity (called strong equivalence in =-=[14]-=-, and inspired by the notion of probabilistic bisimilarity from [17]), defined as follows. Given an RTS with state space X, a stochastic bisimulation is an equivalence relation R on X such that whenev... |

432 | Bisimulation through probabilistic testing
- Larsen, Skou
- 1991
(Show Context)
Citation Context ...ons on states in RTSs have been considered. Of those, the most significant is stochastic bisimilarity (called strong equivalence in [14], and inspired by the notion of probabilistic bisimilarity from =-=[17]-=-), defined as follows. Given an RTS with state space X, a stochastic bisimulation is an equivalence relation R on X such that whenever x R y then for each a ∈ A, and for each equivalence class C with ... |

330 | Universal coalgebra: A theory of systems
- Rutten
(Show Context)
Citation Context ...q to h. For example, for B = (Pω−) A , this span bisimulation specializes to the well-known notion of LTS bisimulation [18]. For more information about the coalgebraic approach to process theory, see =-=[23]-=-. We now show how to view RTSs as coalgebras for a suitable functor on Set. Call a function f : X → R + 0 finitely supported if the set {x ∈ X | f (x) > 0} is finite. For any set X, let RωX be the set... |

212 |
Representation and simulation of biochemical processes using the pi-calculus process algebra
- Regev, Silverman, et al.
- 2001
(Show Context)
Citation Context ...ation proofs, e.g. represented by terms of the grammar: θ = (a, r) | +1θ | +2θ | �1θ | �2θ | 〈�1θ, �2θ〉, and where R depends on r1 and r2 according to the minimal rate law [20] or the mass action law =-=[22]-=-, as in PEPA. These rules are then used to induce an LTS, which results in relatively complex labels. To obtain an RTS, one then extracts more familiar labels a ∈ A from proofs 5 (5) (7)sin the obviou... |

201 |
Bisimulation can’t be traced
- Bloom, Istrail, et al.
- 1995
(Show Context)
Citation Context ...f all terms over Σ with variables from set X is denoted TΣX. In particular, TΣ0 is the set of closed Σ-terms. 2 (1)sFix a countably infinite set Ξ ∋ x, y, z, . . . of variables. A GSOS inference rule =-=[4]-=- over a signature Σ and a set of labels A is an expression of the form � a � � � j bl xi ⊲ y j j xil /⊲ 1≤ j≤k 1≤i≤m c (2) f(x1, . . . , xn) ⊲ t where f ∈ Σ, n = ar(f), k, m ∈ N, i j, il ∈ {1, . . . ,... |

148 | Labeled Markov Process
- Desharnais
- 1999
(Show Context)
Citation Context ...gives rise to a B-coalgebra structure hλ on TΣ0, defined by a “structural recursion theorem” (see [24] for details) as the only function hλ : TΣ0 → BTΣ0 such that: (8) hλ ◦ a = Ba ♯ ◦ λX ◦ Σ〈id, hλ〉. =-=(9)-=- The fact that bisimilarity on LTSs induced from GSOS specifications is guaranteed to be a congruence, can be proved at the level of coalgebras and distributive laws: Theorem 1 ([24], Cor. 7.5). If a ... |

142 | Towards a Mathematical Operational Semantics
- Turi, Plotkin
- 1997
(Show Context)
Citation Context ...eem hard to extend to a general format for well-behaved stochastic specifications, we resolve to adapt a general theory of well-behaved SOS, based on category theory and developed by Turi and Plotkin =-=[24]-=-. The inspiration for our approach comes directly from the work of F. Bartels [2], who used Turi and Plotkin’s results to design a congruence format for probabilistic transition systems.sStandard oper... |

131 | Structural operational semantics
- Aceto, Fokkink, et al.
(Show Context)
Citation Context ...nsition systems (LTSs) are defined by induction on the syntactic structure of processes. Formalisms for SOS decriptions of nondeterministic systems have been widely studied and precisely defined (see =-=[1]-=- for a survey). In particular, several syntactic formats have been developed that guarantee certain desirable properties of the induced systems, most importantly that bisimulation is a congruence on t... |

123 | Multiprocessor and Distributed System Design: The Integration of Functional Specification and Performance Analysis Using Stochastic Process Algebras, in Performance evaluation of computer and communication systems
- Götz, Herzog, et al.
- 1993
(Show Context)
Citation Context ...biology, where the underpinning of labelled continuous time Markov chains (CTMCs), and more generally stochastic processes, is required rather than simple LTSs. Examples of such algebras include TIPP =-=[11]-=-, PEPA [15], EMPA [3], and stochastic π-calculus [20]. Semantics of these calculi have been given by variants of the SOS approach. However, in contrast with the case of nondeterministic processes, SOS... |

105 |
Stochastic π-calculus
- Priami
- 1995
(Show Context)
Citation Context ...s time Markov chains (CTMCs), and more generally stochastic processes, is required rather than simple LTSs. Examples of such algebras include TIPP [11], PEPA [15], EMPA [3], and stochastic π-calculus =-=[20]-=-. Semantics of these calculi have been given by variants of the SOS approach. However, in contrast with the case of nondeterministic processes, SOS formalisms used here are not based on any general fr... |

103 | A tutorial on EMPA: a theory of concurrent processes with n ondet erminism, priorities, probabilities and time
- Bernardo, Gorrieri
- 1998
(Show Context)
Citation Context ...llowing we will consider image-finite processes, i.e. such that for each x ∈ X and a ∈ A there are only finitely many y ∈ X such that ρ(x, a, y) > 0. For such processes, the sum � ρa(x) = ρ(x a −→ y) =-=(3)-=- y∈X exists for each x ∈ X and a ∈ A; it will be called the apparent rate of label a in state x. Further, ρ(x a −→ y)/ρa(x) is called the conditional probability of the transition x a −→ y. It is the ... |

82 | Bisimulation for probabilistic transition systems: a coalgebraic approach
- Vink, Rutten
- 1999
(Show Context)
Citation Context ...defined in §2.2. 7sIn the following, a technical property of the functor (Rω−) A will be useful: Proposition 2. (Rω−) A preserves weak pullbacks. To prove the above two results, proceed exactly as in =-=[7]-=- for the case of probabilistic bisimulation and the corresponding behaviour functor. 3.2 Process syntax via algebras In the context of SOS, processes typically are closed terms over some algebraic sig... |

62 | Process algebra for performance evaluation
- Hermanns, Herzog, et al.
(Show Context)
Citation Context ...n exponential probability distribution governing the duration of the transition of x to y with label a (for more information and intuition on CTMCs and their presentation by transition rates see e.g. =-=[12, 15, 20]-=-). For the sake of readability we will write ρ(x a −→ y) instead of ρ(x, a, y), and x a,r a −→ y will indicate that ρ(x −→ y) = r. The latter notation suggests that RTSs can be seen as a special kind ... |

53 | Automatically deriving ODEs from process algebra models of signalling pathways
- Calder, Gilmore, et al.
(Show Context)
Citation Context ... a ∈ L) is the least of the apparent rates of P and Q. For applications to systems biology, where rates model concentrations of molecules, a more convenient choice is R = r1 · r2, (6) which following =-=[6]-=- we call the mass action law. The apparent rate of a in P ⊲⊳ Q L (with a ∈ L) here is the product of the corresponding apparent rates of P and Q. For an intuitive motivation for these and other simila... |

44 | The Nature of Synchronisation
- Hillston
- 1994
(Show Context)
Citation Context ...s action law. The apparent rate of a in P ⊲⊳ Q L (with a ∈ L) here is the product of the corresponding apparent rates of P and Q. For an intuitive motivation for these and other similar formulae, see =-=[13]-=-. A different approach was used to define semantics of stochastic π-calculus [20]. Since stochastic features of the calculus are independent from its name-passing aspects, for simplicity we discuss it... |

42 | On generalised coinduction and probabilistic specification formats: distributive laws
- Bartels
- 2004
(Show Context)
Citation Context ... we resolve to adapt a general theory of well-behaved SOS, based on category theory and developed by Turi and Plotkin [24]. The inspiration for our approach comes directly from the work of F. Bartels =-=[2]-=-, who used Turi and Plotkin’s results to design a congruence format for probabilistic transition systems.sStandard operations of stochastic process algebras, as well as plenty of non-standard but pote... |

40 | Enhanced operational semantics
- Degano, Priami
- 1996
(Show Context)
Citation Context ... to forbid such inspection altogether, as it is needed, e.g. in the communication rule for stochastic π-calculus. The source of the problem is the richness of labels in the proved approach to SOS. In =-=[8]-=-, it is claimed that proofs as transition labels carry almost all information about processes that is ever needed. Indeed, it appears they may sometimes carry excessive information; in a well-behaved ... |

35 |
Process algebras for quantitative analysis, in
- Hillston
(Show Context)
Citation Context ...ere the underpinning of labelled continuous time Markov chains (CTMCs), and more generally stochastic processes, is required rather than simple LTSs. Examples of such algebras include TIPP [11], PEPA =-=[15]-=-, EMPA [3], and stochastic π-calculus [20]. Semantics of these calculi have been given by variants of the SOS approach. However, in contrast with the case of nondeterministic processes, SOS formalisms... |

20 | A congruence rule format for name-passing process calculi
- Fiore, Staton
- 2009
(Show Context)
Citation Context ...ansition systems. Definition 1. An SGSOS rule for a signature Σ and a set A of labels is an expression of the form: � xi a@rai � � b � j ⊲ xi ⊲ y j j a∈Di,1≤i≤n 1≤ j≤k f(x1, . . . , xn) c@W where ⊲ t =-=(10)-=- – f ∈ Σ and ar(f) = n, with n, k ∈ N, and {i1, . . . , ik} ⊆ {1, . . . , n}; – xi and y j are all distinct variables and no other variables appear in t ∈ TΣΞ; moreover, all variables y j appear in t;... |

8 | Language-based performance prediction for distributed and mobile systems - Priami |

2 |
S.: Probabilistic bisimulation as a congruence
- Lanotte, Tini
- 2009
(Show Context)
Citation Context ...the multi-transition approach in order to guarantee that stochastic bisimilarity is compositional. Indeed, this approach has been used with success in the related framework of probabilistic processes =-=[16]-=-, where a well-behaved version of the proved semantics is developed. In this paper, however, we take a more principled approach and derive a formalism for stochastic operational semantics from an abst... |