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Process Algebra with Probabilistic Choice [chapter]

Suzana Andova
1999 Lecture Notes in Computer Science  
D 12 Process Algebra with Probabilistic Choice Proposition25.  ...  6 Algebra with Probabilistic ChoiceDefinition2.  ... 
doi:10.1007/3-540-48778-6_7 fatcat:p2fmdk2r3rew3az3nqgxjremxq

Probabilistic Observations and Valuations

Matthias Schröder, Alex Simpson
2006 Electronical Notes in Theoretical Computer Science  
We give a universal property for an "abstract probabilistic powerdomain" based on an analysis of observable properties of probabilistic computation.  ...  It follows that our abstract notion of integration coincides with the usual integration with respect to probability valuations.  ...  Definition 2.1 An abstract (probabilistic) choice structure over X is given by a choice algebra (Y, ⊕) together with a map X δ -Y such that Requirement 2 holds.  ... 
doi:10.1016/j.entcs.2005.11.075 fatcat:5f2a7oafhvhshpzbrwplqjzt64

Abstraction in Probabilistic Process Algebra [chapter]

S. Andova, J. C. M. Baeten
2001 Lecture Notes in Computer Science  
Someone familiar with process algebra can easily see the resemblance with the KFAR b 1 rule ( 3]) with non-deterministic choice replaced by probabilistic choice. a) ?>=< 89:; 0  ...  we introduce veri cation rules in fully probabilistic process algebra that arise rather in a natural way from the one de ned in standard process algebra.  ...  Someone familiar with process algebra can easily see the resemblance with the KFAR b 1 rule ( 3]) with non-deterministic choice replaced by probabilistic choice. Fig. 2.  ... 
doi:10.1007/3-540-45319-9_15 fatcat:eu7ag2llovalhapszj7iwlug34

Time and Probability in Process Algebra [chapter]

Suzana Andova
2000 Lecture Notes in Computer Science  
We give two probabilistic process algebras with discrete time.  ...  This process algebra is obtained by extension of untimed probabilistic process algebra with constructors that allow the explicit specification of timing aspects.  ...  First, we extend the Basic process algebra with probabilistic choice ( [1, 2] ) with time constants and time operators.  ... 
doi:10.1007/3-540-45499-3_24 fatcat:mnk3kflmefac7peilyk6am327m

An Overview of Probabilistic Process Algebras and Their Equivalences [chapter]

Natalia López, Manuel Núñez
2004 Lecture Notes in Computer Science  
In order to describe probabilistic processes by means of a formal model, some considerations have to be taken into account.  ...  After that, the different choice operators used in the most common probabilistic languages are enumerated. Once we have an appropriate language, we have to give its semantics.  ...  In the case of process algebras with probabilistic information these two decisions are far from obvious. Specifically, in order to model the choice there are several possibilities.  ... 
doi:10.1007/978-3-540-24611-4_3 fatcat:cb5v35j7bbay3g6njscpafbm5i

On Combining Probability and Nondeterminism

M.W. Mislove
2006 Electronical Notes in Theoretical Computer Science  
Early work used schedulers to model probabilistic choice, interleaving their execution with that of nondeterministic choice, a theme that continues in some operational models today.  ...  More recent work has focused on providing a principled account of the interactions of these operators, with the aim of devising models that support both operators so that neither is related with the other  ...  Introduction Nondeterminism has been a staple of process algebra since its inception, but more recently probabilistic choice has been included.  ... 
doi:10.1016/j.entcs.2005.12.113 fatcat:c4itrys7jzftnjlc52uahqmkc4

Process Model to Predict Nondeterministic Behavior of IoT Systems

Yeongbok Choe, Moonkun Lee
2018 The Practice of Enterprise Modeling  
There have been several process algebras with probability, such as, PAROMA, PACSR, etc.  ...  Process algebra is one of the best suitable formal methods to model IoT systems, supporting formal specification and analysis.  ...  Generally, it is very difficult to predict various system behaviors with process algebra because of its nondeterministic choice operations.  ... 
dblp:conf/ifip8-1/ChoeL18 fatcat:ejp6p57o7ja7licpma26yv7s7q

Axiomatization of trace semantics for stochastic nondeterministic processes

A. Parma, R. Segala
2004 First International Conference on the Quantitative Evaluation of Systems, 2004. QEST 2004. Proceedings.  
We give a complete axiomatization of trace distribution precongruence for probabilistic nondeterministic processes based on a process algebra that includes internal behavior and recursion.  ...  The axiomatization is given for two different semantics of the process algebra that are consistent with the alternating model of Hansson and the non-alternating model of Segala, respectively.  ...  We consider a process algebra with nondeterministic choice, probabilistic choice, and recursion, that is, an algebra that extends classical process algebras with just one new operator that models probability  ... 
doi:10.1109/qest.2004.1348043 dblp:conf/qest/ParmaS04 fatcat:qdpthwdklfhiph36qtctq3u3nu

Instruction sequence notations with probabilistic instructions [article]

J. A. Bergstra, C. A. Middelburg
2014 arXiv   pre-print
This paper concerns instruction sequences that contain probabilistic instructions, i.e. instructions that are themselves probabilistic by nature.  ...  We propose several kinds of probabilistic instructions, provide an informal operational meaning for each of them, and discuss related work.  ...  The first probabilistic process algebra is presented in [23] and the first probabilistic process algebra with an asynchronous parallel composition operator is presented in [5] .  ... 
arXiv:0906.3083v2 fatcat:bsfhmph2bvhz3b4axci2dsn75q

Probabilistic Branching in Markovian Process Algebras

M. Rettelbach
1995 Computer journal  
We introduce immediate transitions as an extension of Stochastic Process Algebras (SPA).  ...  Although we use TIPP as a sample language within this paper, the theory can easily be adapted to other Stochastic Process Algebras and can therefore be seen as a general result for probabilistic branching  ...  INTRODUCTION AND MOTIVATION Recent research on the algebraic theory for Stochastic Process Algebras (SPA) has concentrated on Markovian durations associated with each activity.  ... 
doi:10.1093/comjnl/38.7.590 fatcat:vpsusbqiwja2ziovnm6w4u5eli

Using Probabilistic Kleene Algebra for Protocol Verification [chapter]

A. K. McIver, E. Cohen, C. C. Morgan
2006 Lecture Notes in Computer Science  
We propose a method for verification of probabilistic distributed systems in which a variation of Kozen's Kleene Algebra with Tests [11] is used to take account of the well-known interaction of probability  ...  We describe pKA, a probabilistic Kleene-style algebra, based on a widely accepted model of probabilistic/demonic computation [7, 25, 17] .  ...  his choice of which process to schedule, based on the result of a previous probabilistic choice.  ... 
doi:10.1007/11828563_20 fatcat:nlh7zni2bzgtnaws4uuoze6nve

Probabilistic process algebra and strategic interleaving [article]

C. A. Middelburg
2020 arXiv   pre-print
resolved and then extend this probabilistic version of ACP with a form of interleaving in which parallel processes are interleaved according to what is known as a process-scheduling policy in the field  ...  We first present a probabilistic version of ACP that rests on the principle that probabilistic choices are always resolved before choices involved in alternative composition and parallel composition are  ...  pACP with Guarded Recursion In this section, we introduce pACP (probabilistic Algebra of Communicating Processes) and guarded recursion in the setting of pACP.  ... 
arXiv:1912.10041v6 fatcat:hvtnwm6alfc4jegnc5hbvmdkky

Using probabilistic Kleene algebra pKA for protocol verification

A.K. McIver, C. Gonzalia, E. Cohen, C.C. Morgan
2008 The Journal of Logic and Algebraic Programming  
We propose a method for verification of probabilistic distributed systems in which a variation of Kozen's Kleene Algebra with Tests [Dexter Kozen, Kleene algebra with tests, ACM Trans.  ...  We describe pKA, a probabilistic Kleene-style algebra, based on a widely accepted model of probabilistic/demonic computation [Jifeng He, K. Seidel, A.K.  ...  his choice of which process to schedule, based on the result of a previous probabilistic choice.  ... 
doi:10.1016/j.jlap.2007.10.005 fatcat:nuuhuzvb3bgrlcqykiw7opbw7a

Page 7071 of Mathematical Reviews Vol. , Issue 2003i [page]

2003 Mathematical Reviews  
Summary: “We present a process algebra expressing probabilistic external/internal choices, multi-way synchronizations, and pro- cesses with different advancing speeds in the context of discrete time, i.e  ...  Summary: “The modeling and analysis experience with process al- gebras has shown the necessity of extending them with priority, probabilistic internal/external choice, and time while preserving compositionality  ... 

A probabilistic choice model based on Tsallis' statistics

Taiki Takahashi
2007 Physica A: Statistical Mechanics and its Applications  
This paper proposes a probabilistic choice model based on a mathematical equivalence of delay and uncertainty in decision-making, and the deformed algebra developed in the Tsallis' non-extensive thermodynamics  ...  Decision under risk and uncertainty (probabilistic choice) has been attracting attention in econophysics and neuroeconomics.  ...  In order to develop decision theory on probabilistic choice, recent efforts in neuroeconomics have started to combine probabilistic choice processes with intertemporal choice process [4] .  ... 
doi:10.1016/j.physa.2007.07.005 fatcat:q36zhfzplzfyhovd2tauzduise
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