“…If inhibitor arcs are not involved, to represent transitions by their beginnings and ends we might just replace each transition t by the net Bt Et i E E t as proposed for example by Zuberek in [Zuberek [1980]] for Timed Petri nets. However, the inhibitor arcs cause some problems.…”
When system runs are modeled with interval orders, interval order structures are useful tools to model abstract concurrent histories, i.e. sets of equivalent system runs. For the general cases, Mazurkiewicz traces allow a representation of the entire partial order by a single sequence with independency relations, and Comtraces allow a representation of stratified order structures by single step sequences with appropriate simultaneity and serializability relations. Unfortunately, both of them are unable to clearly describe the abstract interval order semantics of inhibitor nets.The goal of the thesis is to provide a monoid based model called Interval Traces that would allow a single sequence of beginnings and endings to represent the entire stratified order structures as well as all equivalent interval order observations. And the thesis will also show how interval order structures can be modelled by interval traces and how interval traces can be used to describe interval order semantics.
“…If inhibitor arcs are not involved, to represent transitions by their beginnings and ends we might just replace each transition t by the net Bt Et i E E t as proposed for example by Zuberek in [Zuberek [1980]] for Timed Petri nets. However, the inhibitor arcs cause some problems.…”
When system runs are modeled with interval orders, interval order structures are useful tools to model abstract concurrent histories, i.e. sets of equivalent system runs. For the general cases, Mazurkiewicz traces allow a representation of the entire partial order by a single sequence with independency relations, and Comtraces allow a representation of stratified order structures by single step sequences with appropriate simultaneity and serializability relations. Unfortunately, both of them are unable to clearly describe the abstract interval order semantics of inhibitor nets.The goal of the thesis is to provide a monoid based model called Interval Traces that would allow a single sequence of beginnings and endings to represent the entire stratified order structures as well as all equivalent interval order observations. And the thesis will also show how interval order structures can be modelled by interval traces and how interval traces can be used to describe interval order semantics.
“…Some of them are suitable to do performance evaluations, since the time is represented as a fixed delay or time durations (Ramchandani, 1974;Sifakis, 1980;Zuberek, 1980). However, those Petri nets models are not well suited to deal with real-time systems where the time duration of activities (or tasks) could not be predicted.…”
“…For instance, neither Milner's CCS [23], Hoare's CSP [18], nor Petri Nets [31], in their original form, were concerned with temporal behavior but they all have been extended to incorporate an explicit notion of time. Namely, Timed CCS [52], Timed CSP [34], and Timed Petri Nets [53].…”
Concurrent constraint programming (ccp) is a model of concurrency for systems in which agents (also called processes) interact with one another by telling and asking information in a shared medium. Timed (or temporal) ccp extends ccp by allowing agents to be constrained by time requirements. The novelty of timed ccp is that it combines in one framework an operational and algebraic view based upon process calculi with a declarative view based upon temporal logic. This allows the model to benefit from two well-established theories used in the study of concurrency. This essay offers an overview of timed ccp covering its basic background and central developments. The essay also includes an introduction to a temporal ccp formalism called the ntcc calculus.
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