Enrique Teruel

Linear Algebraic and Linear Programming Techniques for the Analysis of Place or Transition Net Systems

The structure theory of Place/Transition net systems is surveyed — incorporating new contributions — in a tutorial style, mainly from a linear algebraic perspective. Topics included are: state equation based analysis of safety properties (e.g., boundedness, mutual exclusion, deadlock-freeness, etc.), linear invariants, siphons and traps, implicit places and their application to improve the accuracy of the state equation, and rank theorems (structural conditions for liveness and boundedness based on the rank of the incidence matrix).

On Weighted T-Systems

Structure theory is a branch of net theory devoted to investigate the relationship between the structure and the behaviour of net system models. Many of its powerful results have been derived for some subclasses of ordinary net systems. The aim of this contribution is to draw a general perspective of the structure theory for a subclass with Marked Graph-like underlying graph but allowing weights: weighted T-graphs (WTG). Weights are convenient to properly model systems with bulk services and arrivals. Properties of WTG and the corresponding weighted T-systems (WTS) are presented at three different levels: purely structural (e.g. in consistent WTG conservativeness is equivalent to strong connectedness), inter-relationships between the structure and the behaviour (e.g. structural liveness and boundedness is equivalent to consistency and strong connectedness) and liveness and reachability characterizations (e.g. deciding liveness is linear wrt. the 1-norm of the unique minimal T-semiflow of a consistent, even unbounded, WTS). Classical results for Marked Graphs can be derived as corollaries. Nevertheless, even in live and consistent WTS, important properties of Marked Graphs do not hold (e.g. P-semiflows based characterization of reachability).

Petri Nets for the Design and Operation of Manufacturing Systems

Modern manufacturing systems pose a diversity of problems all along their life cycle which are often treated with particular independent formalisms and techniques. Petri nets are a family of formalisms which can be used, sometimes with advantage, for many of these problems, with the additional benefit of improving the communication between stages of the life cycle. The utilisation of Petri nets in several of these stages is illustrated and surveyed in this paper, mainly addressed to manufacturing systems engineers with a basic knowledge of Petri nets.

Autonomous Continuous P/T Systems

Discrete event dynamic systems may have extremely large state spaces. For their analysis, it is usual to relax the description by removing the integrality constraints. Applying this idea, continuous P/T systems are defined by allowing fractional firings of transitions, and thus the existence of non-discrete markings [4,5,1]. In this paper we compare the behaviors of discrete and continuous systems, and observe that they are not necessarily similar. The problems that appear lead to the definition of two extensions of reachability. Many properties shall be extended differently depending on which reachability definition is being considered. Here, we concentrate on liveness and deadlock-freeness, proposing extensions and relating them to their discrete counterparts.

Choice-free Petri nets: a model for deterministic concurrent systems with bulk services and arrivals

Among discrete event systems, those exhibiting concurrency are especially challenging, requiring the use of formal methods to deal with them. Petri nets are a well-established such formalism. The structure theory aims at overcoming the state space explosion problem, inherent to the analysis of concurrent systems, by bridging structural and behavioral properties. To date, this has been successfully achieved mainly for some subclasses of ordinary nets. However weights are a modeling convenience in many situations. In this paper we study a formal model for a subclass of concurrent systems with bulk services and arrivals which structurally avoids conflicts. Structural results and techniques for dealing with them are introduced. These include structural conditions on properties of correct behavior and a unified framework for checking general behavioral properties by reasoning solely on the structure.

Structure theory of equal conflict systems

Abstract Equal conflict net systems are a weighted generalisation of the (extended) free choice subclass that keeps the total autonomy of choices. A substantial part of the analytical branch of the structure theory of free choice systems, including decomposition and duality, the rank theorem, characterisations of impartial sequences and prompt interfaces, and the existence of home states, is extended to the equal conflict case. In so doing, several familiar concepts and objects from the structure theory of place/transition net systems are revisited from a linear algebraic perspective, which is specially adequate to cope with weighted nets.

Liveness and Home States in Equal Conflict Systems

Structure theory is a branch of net theory devoted to investigate the relationship between the structure and the behaviour of net models. Many of its powerful results have been derived for some subclasses of ordinary (i.e. all weights one) Place/Transition net systems. Nevertheless, weights may be very convenient to properly model systems with bulk services and arrivals. They can be implemented by means of ordinary subnets, but then the original structure of the net becomes too complex, even in the simplest cases, to be amenable of some interesting structural analysis techniques.

Modeling and analysis of sequential processes that cooperate through buffers

Deterministically synchronized sequential processes (DSSP) are a subclass of Petri nets, well suited for the methodical construction of models of concurrent systems where several agents cooperate through asynchronous message passing, In this paper, DSSP are presented, illustrating their usability in manufacturing systems. They are compared to other more restrictive subclasses of Petri nets used for similar purposes. In spite of being more expressive, DSSP still enjoy many strong analytical results, some of which are derived and illustrated in the paper.

Petri Nets and Production Systems

Modern production systems pose a diversity of problems all along their life cycle which are often treated with particular independent formalisms and techniques. Production systems can be viewed as discrete event, continuous, or hybrid systems. Petri nets are a family of formalisms which can be used for the modelling, analysis, implementation and control of these systems, with the benefit of improving the communication between stages of the life cycle.

ON LINEAR ALGEBRAIC TECHNIQUES FOR LIVENESS ANALYSIS OF P/T SYSTEMS

Liveness is a basic property that in many discrete event dynamic systems is considered essential for their correct behavior. It expresses that no action (transition in P/T models) will ever become unattainable. A polynomial time necessary condition for the existence of a live and bounded marking of a P/T net is given. This condition is shown to be also sufficient for some subclasses. The applicability of these results is extended by the use of transformation techniques that allow for their exploitation in the analysis of more general nets. Some results for the structural analysis of actual liveness are also overviewed, in particular, sufficient conditions for deadlock-freeness and absence of dead transitions.