Łukasz Mikulski

A taxonomy of persistent and nonviolent steps

A concurrent system is persistent if throughout its operation no activity which became enabled can subsequently be prevented from being executed by any other activity. This is often a highly desirable (or even necessary) property; in particular, if the system is to be implemented in hardware. Over the past 40 years, persistence has been investigated and applied in practical implementations assuming that each activity is a single atomic action which can be represented, for example, by a single transition of a Petri net. Recently, it turned out that to deal with the synthesis of GALS systems one also needs to consider activities represented by steps, each step being a set of simultaneously executed transitions. Moving into the realm of step based execution, semantics creates a wealth of new fundamental problems and questions. In particular, there are different ways in which the standard notion of persistence could be lifted from the level of sequential semantics to the level of step semantics. Moreover, one may consider steps which are persistent and cannot be disabled by other steps, as well as steps which are nonviolent and cannot disable other steps. In this paper, we provide a classification of different types of persistence and nonviolence, both for steps and markings of pt-nets. We also investigate behavioural and structural properties of such notions.

Reversible computation vs. reversibility in Petri nets

Abstract Petri nets are a general formal model of concurrent systems which supports both action-based and state-based modelling and reasoning. One of important behavioural properties investigated in the context of Petri nets has been reversibility, understood as the possibility of returning to the initial marking from any reachable net marking. Thus reversibility in Petri nets is a global property. Reversible computation, on the other hand, is typically a local mechanism by which a system can undo some of the executed actions. This paper is concerned with the modelling of reversible computation within Petri nets. A key idea behind the proposed construction is to add ‘reverses’ of selected transitions, and the paper discusses its different implementations. Adding reverses can severely impact on the behaviour of a Petri net. Therefore it is important, in particular, to be able to determine whether the modified net has a similar set of states as the initial one. We first prove that the problem of establishing whether the initial and modified nets have the same reachable markings is undecidable, even in the restricted case considered in this paper. We then show that the problem of checking whether the reachability sets of the two nets cover the same markings is decidable.

Reversing Transitions in Bounded Petri Nets

Reversible computation deals with mechanisms for undoing the effects of actions executed by a dynamic system. This paper is concerned with reversibility in the context of Petri nets which are a general formal model of concurrent systems. A key construction we investigate amounts to adding ‘reverse’ versions of selected net transitions. Such a static modification can severely impact on the behaviour of the system, e.g., the problem of establishing whether the modified net has the same states as the original one is undecidable. We therefore concentrate on nets with finite state spaces and show, in particular, that every transition in such nets can be reversed using a suitable finite set of new transitions.

Algebraic structure of combined traces

Traces --- and their extension called combined traces (comtraces) --- are two formal models used in the analysis and verification of concurrent systems. Both models are based on concepts originating in the theory of formal languages, and they are able to capture the notions of causality and simultaneity of atomic actions which take place during the process of a systems operation. The aim of this paper is a transfer to the domain of comtraces and developing of some fundamental notions, which proved to be successful in the theory of traces. In particular, we introduce and then apply the lexicographical canonical form of comtraces, as well as the representation of a comtrace utilising its linear projections to binary action subalphabets. We also provide two algorithms related to the new notions. Using them, one can solve, in an efficient way, the problem of step sequence equivalence in the context of comtraces. One may view our results as a first step towards the development of infinite combined traces, as well as recognisable languages of combined traces.

Order Structures for Subclasses of Generalised Traces

Traces are equivalence classes of action sequences which can be represented by partial orders capturing the causality in the behaviour of a concurrent system. Generalised traces, on the other hand, are equivalence classes of step sequences. They are represented by order structures that can describe non-simultaneity and weak causality, phenomena which cannot be expressed by partial orders alone. In this paper, we provide a systematic classification of different subclasses of generalised traces in terms of the order structures representing them. We also show how the original trace model fits into the overall framework.

Characterising Concurrent Histories

Non-interleaving semantics of concurrent systems is often expressed using posets, where causally related events are ordered and concurrent events are unordered. Each causal poset describes a unique concurrent history, i.e., a set of executions, expressed as sequences or step sequences, that are consistent with it. Moreover, a poset captures all precedence-based invariant relationships be- tween the events in the executions belonging to its concurrent history. However, concurrent histories in general may be too intricate to be described solely in terms of causal posets. In this paper, we introduce and investigate generalised mutex order structures which can capture the invariant causal relationships in any concurrent history consisting of step sequence executions. Each such structure comprises two relations, viz. interleaving/mutex and weak causality. As our main result we prove that each generalised mutex order structure is the intersection of the step sequence executions which are consistent with it.

Reversible Computation vs. Reversibility in Petri Nets

Petri nets are a general formal model of concurrent systems which supports both action-based and state-based modelling and reasoning. One of important behavioural properties investigated in the context of Petri nets has been reversibility, understood as the possibility of returning to the initial marking from any reachable net marking. Thus reversibility in Petri nets is a global property. Reversible computation, on the other hand, is typically a local mechanism using which a system can undo some of the executed actions. This paper is concerned with the modelling of reversible computation within Petri nets. A key idea behind the proposed construction is to add ‘reverse’ versions of selected transitions. Since such a modification can severely impact on the behavior of the system, it is crucial, in particular, to be able to determine whether the modified system has a similar set of states as the original one. We first prove that the problem of establishing whether the two nets have the same reachable markings is undecidable even in the restricted case discussed in this paper. We then show that the problem of checking whether the reachability sets of the two nets cover the same markings is decidable.

Conditions for Petri Net Solvable Binary Words

A word is called Petri net solvable if it is isomorphic to the reachability graph of an unlabelled Petri net. In this paper, the class of finite, two-letter, Petri net solvable, words is studied. Two conjectures providing different characterisations of this class of words are motivated and proposed. One conjecture characterises the class in terms of pattern-matching, the other in terms of letter-counting. Several results are described which amount to a partial proof of these conjectures.

On Generation of Context-Abstract Plans

This paper deals with an intermediate phase of resolving Web Service Composition Problem (WSCP) provided by Planics. The abstract planner discovers a set of abstract plans for a WSCP instance. The proposed algorithm utilizes the combinatorial structure of this set and, abstracting from object attributes, browses the space of all potential solutions taking into account only indistinguishable ones. Finally, the reported results are validated by checking the attributes valuation and presumed constraints.

Asynchronous parallel molecular dynamics simulations

Dynamic development of parallel computers makes them standard tool for large simulations. The technology achievements are not followed by the progress in scalable code design. The molecular dynamics is a good example. In this paper we present novel approach to the molecular dynamics which is based on the new asynchronous parallel algorithm inspired by the novel computer architectures. We present also implementation of the algorithm written in Java. Presented code is object-oriented, multithread and distributed. The performance data is also available.