Elementary transition systems

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Femtosecond transition-state dynamics

This article presents the progress made in probing femtosecond transition–state dynamics of elementary reactions. Experiments demonstrating the dynamics in systems characterized by a transition region and by a saddle-point transition state are reported, and comparison with theory is made

Transition System Models for Concurrency

Labelled transition systems can be extended to faithfully model concurrency by permitting transitions between states to be labelled by a collection of actions, denoting a concurrent step, We can characterize a subclass of these step transition systems, called PN-transition systems, which describe the behaviour of Petri nets.This correspondence is formally described in terms of a coreflection between a category of PN-transition systems and a category of Petri nets.In this paper, we show that we can define subcategories of PN-transition systems whose objects are safe PN-transition systems and elementary PN-transition systems such that there is a coreflection between these subcategories and subcategories of our category of Petri nets corresponding to safe nets and elementary net systems.We also prove that our category of elementary PN-transition systems is equivalent to the category of (sequential) elementary transition systems defined by Nielsen, Rozenberg and Thiagarajan, thereby establishing that the concurrent behaviour of an elementary net system can be completely recovered from a description of its sequential behaviour. Finally, we establish a coreflection between our category of safe PN-transition system and a subcategory of asynchronous transition systems which has been shown by Winskel and Nielsen to be closely linked to safe nets

Transition Systems, Event Structures and Unfoldings

Elementary transition systems were introduced by the authors in DAIMI PB-310. They were proved to be, in a strong categorical sense, the transition system version of elementray net systems. The question arises whether the notion of a region and the axioms (mostly based on regions) imposed on ordinary transition systems to obtain elementray net systems. Stated differently, one colud ask whether elementray transition systems could also play a role in characterizing other models of concurrency. We show here that by smoothly stengthening the axioms of elementary transition systems one obtains a subclass called occurrence transitions systems which turn out to be categorically equivalent to the well-known model of concurrency called prime event structures. Next we show that occurrence transition systems are to elementry transition systems what occurrence nets are to elementary nets systems. We define an ''unfold'' operation on elementry transition systems which yields occurrence transistion systems. We then prove that this operation uniquely extends to a functor which is the right adjoint to the inclusion functor from (the full subcategory of) occurrence transition systems to (the category of) elementary transition systems. Thus the results of this paper also show that the semantic theory of elementray net systems has a nice counterpart in the more abstract world of transition systems

Higher Dimensional Transition Systems

We introduce the notion of higher dimensional transition systems as a model of concurrency providing an elementary, set-theoretic formalisation of the idea of higher dimensional transition. We show an embedding of the category of higher dimensional transition systems into that of higher dimensional automata which cuts down to an equivalence when we restrict to non-degenerate automata. Moreover, we prove that the natural notion of bisimulation for such structures is a generalisation of the strong history preserving bisimulation, and provide an abstract categorical account of it via open maps. Finally, we define a notion of unfolding for higher dimensional transition systems and characterise the structures so obtained as a generalisation of event structures

Elementary Transition Systems and Refinement

The model of Elementary Transition Systems has been introduced by the authors as an abstraction of Elementary Net Systems - with a formal embedding in terms of a categorical coreflection, keeping behavioural information like causality, concurrency and conflict, but forgetting the concrete programming of a particular behaviour over an event set using conditions. In this paper we give one example of the advantages of ETS over ENS, - the definition of local state refinement. We show that the well known problems in understanding within nets the simple notion of syntactic substitution of conditions by (sub) nets behaviourally, - these problems seem to disappear when moving to the more abstract level of ETS. Formally, we show that the ETS-version of condition-substitution does satisfy nice and natural properties, e.g., projection and compositionality results w.r.t. a standard notion of transition system morphisms

Elementary Transition Systems and Refinement

The model of Elementary Transition Systems has been introduced by the authors as an abstraction of Elementary Net Systems - with a formal embedding in terms of a categorical coreflection, keeping behavioural information like causality, concurrency and conflict, but forgetting the concrete programming of a particular behaviour over an event set using conditions. In this paper we give one example of the advantages of ETS over ENS, - the definition of local state refinement. We show that the well known problems in understanding within nets the simple notion of syntactic substitution of conditions by (sub) nets behaviourally, - these problems seem to disappear when moving to the more abstract level of ETS. Formally, we show that the ETS-version of condition-substitution does satisfy nice and natural properties, e.g., projection and compositionality results w.r.t. a standard notion of transition system morphisms

Elementary Transition Systems and Refinement

The model of Elementary Transition Systems has been introduced by the authors as an abstraction of Elementary Net Systems - with a formal embedding in terms of a categorical coreflection, keeping behavioural information like causality, concurrency and conflict, but forgetting the concrete programming of a particular behaviour over an event set using conditions. In this paper we give one example of the advantages of ETS over ENS, - the definition of local state refinement. We show that the well known problems in understanding within nets the simple notion of syntactic substitution of conditions by (sub) nets behaviourally, - these problems seem to disappear when moving to the more abstract level of ETS. Formally, we show that the ETS-version of condition-substitution does satisfy nice and natural properties, e.g., projection and compositionality results w.r.t. a standard notion of transition system morphisms

Some complexity results on transition systems and elementary net systems

AbstractThere is a strong relationship between transition systems and elementary net systems. We consider the problem of finding an elementary net system corresponding to a given transition systems, where the correspondence is defined as an isomorphism between a transition system and the state transition diagram of an EN system. The problem is decomposed into two related problems, and we show that these problems are NP-complete. However, this result does not mean that the original problem is NP-complete. The problem to construct a labeled EN system corresponding to a given transition system is also considered