Separation logic is an extension of Hoare’s logic which supports a local way of reasoning about programs that mutate memory. We present a study of the semantic structures lying behind the logic. The core idea is of a local action, a state transformer that mutates the state in a local way. We formulate local actions for a general class of models called separation algebras, abstracting from the RAM and other specific concrete models used in work on separation logic. Local actions provide a semantics for a generalized form of (sequential) separation logic. We also show that our conditions on local actions allow a general soundness proof for a separation logic for concurrency, interpreted over arbitrary separation algebras.

Electronic commerce is emerging as one of the major Websupported applications requiring database support. We introduce and study high-level declarative specifications of business models, using an approach in the spirit of active databases. More precisely, business models are specified as relational transducers that map sequences of input relations into sequences of output relations. The semantically meaningful trace of an input-output exchange is kept as a sequence of log relations. We consider problems motivated by electronic commerce applications, such as log validation, verifying temporal properties of transducers, and comparing two relational transducers. Positive results are obtained for a restricted class of relational transducers called Spocus transducers (for semi-positive outputs and cumulative state). We argue that despite the restrictions, these capture a wide range of practically significant business models. 1 Introduction Electronic commerce is emerging as a major Web-s...

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In this paper we formulate asynchronous diagnosis by means of hidden state history reconstruction, from alarm observations. We follow a so-called true concurrency approach, in which no global state and no global time is available. Instead, we use only local states in combination with a partial order model of time, in which local events are ordered if they are either generated on the same site, or related via some causality relation. Our basic mathematical tool is that of net unfoldings originating from the Petri net research area. This study was motivated by the problem of event correlation in telecommunications network management.

Abstract. We present an extension of a Petri net semantics for the Web Service Business Execution Language (WS-BPEL). This extension covers the novel activities and constructs introduced by the recent WS-BPEL 2.0 specification. Furthermore, we simplify several aspects of the Petri net semantics to allow for more compact models suited for computer-aided verification.

The main feature of zero-safe nets is a primitive notion of transition synchronization. To this aim, besides ordinary places, called stable places, zero-safe nets are equipped with zero places, which in an observable marking cannot contain any token. This yields the notion of transaction: a basic atomic computation, which may use zero tokens as triggers, but defines an evolution between observable markings only. The abstract counterpart of a generic zero-safe net B consists of an ordinary P/T net whose places are the stable places of B, and whose transitions represent the transactions of B. The two nets offer both the refined and the abstract model of the same system, where the former can be much smaller than the latter, because of the transition synchronization mechanism. Depending on the chosen approach -- collective vs individual token philosophy -- two notions of transaction may be defined, each leading to different operational and abstract models. Their comparison is fully dis...

This report describes a method for constructing a Petri net controller for a discrete event system modeled by a Petri net. The controller consists only of places and arcs and is computed based on the concept of place invariants of the net. The size of the controller is proportional to the number of the constraints which must be satisfied. This method can accommodate constraints written as logic formulas, algebraic inequalities or equalities. Keywords: Discrete Event Systems, Petri Nets 1 Introduction Petri nets are a very appropriate tool for the study of discrete-event dynamical systems because of their power and flexibility. In the past they have been used extensively to model and simulate many kinds of systems . Their use in control is somewhat limited and only recently some studies have been conducted towards this direction [1, 2, 4]. Holloway and Krogh [1] used controlled Petri nets to control systems that can be modeled as cyclic controlled marked graphs, which is a special clas...

. We present a Petri net based framework called G-Net for the modular design of complex information systems. The motivation of this framework is to integrate Petri net theory with a modular, objectoriented approach for the specification and prototyping of complex software systems. We use the client/server example to illustrate the G-Net specification of distributed systems, and how such a specification can be translated into a Predicate/Transition net for formal analysis. The differences between G-Net and hierarchical Petri net, as well as some limitations of the transformation technique, are then discussed. 1 Introduction First introduced by C.A. Petri in the early sixties, Petri nets have been actively studied and applied to many areas of computer science. Different variations or extensions of Petri nets have been proposed. The early Condition/Event (CE) nets and their extension, Place/Transition nets, serve as the basis for other higher level or more specialized Petri net ...

A supervisor synthesis technique for Petri net plants with uncontrollable and unobservable transitions that enforces the conjunction of a set of linear inequalities on the reachable markings of the plant is presented. The approach is based on the concept of Petri net place invariants. Each step of the procedure is illustrated through a running example involving the supervision of a robotic assembly cell. The controller is described by an auxiliary Petri net connected to the plant's transitions, providing a unified Petri net model of the closed loop system. The synthesis technique is based on the concept of admissible constraints. An inadmissible constraint can not be directly enforced on a plant due to the uncontrollability or unobservability of certain plant transitions. Procedures are given for identifying all admissible linear constraints for a plant with uncontrollable and unobservable transitions, as well as methods for transforming inadmissible constraints into admissib...

. In the last few years, the semantics of Petri nets has been investigated in several di#erent ways. Apart from the classical "token game," one can model the behaviour of Petri nets via non-sequential processes, via unfolding constructions, which provide formal relationships between nets and domains, and via algebraic models, which view Petri nets as essentially algebraic theories whose models are monoidal categories. In this paper we show that these three points of view can be reconciled. In our formal development a relevant role is played by DecOcc, a category of occurrence nets appropriately decorated to take into account the history of tokens. The structure of decorated occurrence nets at the same time provides natural unfoldings for Place/Transition (PT) nets and suggests a new notion of processes, the decorated processes, which induce on Petri nets the same semantics as that of unfolding. In addition, we prove that the decorated processes of a net can be axiomatized as the arrows...