Priorities Without Priorities: Representing Preemption in Psi-Calculi

Psi-calculi is a parametric framework for extensions of the pi-calculus with data terms and arbitrary logics. In this framework there is no direct way to represent action priorities, where an action can execute only if all other enabled actions have lower priority. We here demonstrate that the psi-calculi parameters can be chosen such that the effect of action priorities can be encoded. To accomplish this we define an extension of psi-calculi with action priorities, and show that for every calculus in the extended framework there is a corresponding ordinary psi-calculus, without priorities, and a translation between them that satisfies strong operational correspondence. This is a significantly stronger result than for most encodings between process calculi in the literature. We also formally prove in Nominal Isabelle that the standard congruence and structural laws about strong bisimulation hold in psi-calculi extended with priorities.Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127

Read Operators and their Expressiveness in Process Algebras

We study two different ways to enhance PAFAS, a process algebra for modelling asynchronous timed concurrent systems, with non-blocking reading actions. We first add reading in the form of a read-action prefix operator. This operator is very flexible, but its somewhat complex semantics requires two types of transition relations. We also present a read-set prefix operator with a simpler semantics, but with syntactic restrictions. We discuss the expressiveness of read prefixes; in particular, we compare them to read-arcs in Petri nets and justify the simple semantics of the second variant by showing that its processes can be translated into processes of the first with timed-bisimilar behaviour. It is still an open problem whether the first algebra is more expressive than the second; we give a number of laws that are interesting in their own right, and can help to find a backward translation.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407

Adding Priority to Event Structures

Event Structures (ESs) are mainly concerned with the representation of causal relationships between events, usually accompanied by other event relations capturing conflicts and disabling. Among the most prominent variants of ESs are Prime ESs, Bundle ESs, Stable ESs, and Dual ESs, which differ in their causality models and event relations. Yet, some application domains require further kinds of relations between events. Here, we add the possibility to express priority relationships among events. We exemplify our approach on Prime, Bundle, Extended Bundle, and Dual ESs. Technically, we enhance these variants in the same way. For each variant, we then study the interference between priority and the other event relations. From this, we extract the redundant priority pairs-notably differing for the types of ESs-that enable us to provide a comparison between the extensions. We also exhibit that priority considerably complicates the definition of partial orders in ESs.Comment: In Proceedings EXPRESS/SOS 2013, arXiv:1307.690

Checking progress with aAction priority: is it fair?

The liveness characteristics of a system are intimately related to the notion of fairness. However, the task of explicitly modelling fairness constraints is complicated in practice. To address this issue, we propose to check LTS (Labelled Transition System) models under a strong fairness assumption, which can be relaxed with the use of action priority. The combination of the two provides a novel and practical way of dealing with fairness. The approach is presented in the context of a class of liveness properties termed progress, for which it yields a particularly efficient model-checking algorithm. Progress properties cover a wide range of interesting properties of systems, while presenting a clear intuitive meaning to users

The Mathematical Abstraction Theory, The Fundamentals for Knowledge Representation and Self-Evolving Autonomous Problem Solving Systems

The intention of the present study is to establish the mathematical fundamentals for automated problem solving essentially targeted for robotics by approaching the task universal algebraically introducing knowledge as realizations of generalized free algebra based nets, graphs with gluing forms connecting in- and out-edges to nodes. Nets are caused to undergo transformations in conceptual level by type wise differentiated intervening net rewriting systems dispersing problems to abstract parts, matching being determined by substitution relations. Achieved sets of conceptual nets constitute congruent classes. New results are obtained within construction of problem solving systems where solution algorithms are derived parallel with other candidates applied to the same net classes. By applying parallel transducer paths consisting of net rewriting systems to net classes congruent quotient algebras are established and the manifested class rewriting comprises all solution candidates whenever produced nets are in anticipated languages liable to acceptance of net automata. Furthermore new solutions will be added to the set of already known ones thus expanding the solving power in the forthcoming. Moreover special attention is set on universal abstraction, thereof generation by net block homomorphism, consequently multiple order solving systems and the overall decidability of the set of the solutions. By overlapping presentation of nets new abstraction relation among nets is formulated alongside with consequent alphabetical net block renetting system proportional to normal forms of renetting systems regarding the operational power. A new structure in self-evolving problem solving is established via saturation by groups of equivalence relations and iterative closures of generated quotient transducer algebras over the whole evolution.Comment: This article is a part of my thesis giving the unity for both knowledge presentation and self-evolution in autonomous problem solving mathematical systems and for that reason draws heavily from my previous work arxiv:1305.563