Derivation Languages of Graph Grammars

We investigate sequential derivation languages associated with graph grammars, as a loose generalisation of free-labeled Petri nets and Szilard languages. The grammars are used to output strings of rule labels, and the applicability of a special rule determines the acceptance of a preceding derivation.Due to the great power of such grammars, this family of languages is quite large and endowed with many closure properties. All derivation languages are decidable in nondeterministic polynomial time and space O(n log n), by simulation of the graph grammar on a Turing machine

Theoretical Aspects of Computing (ICTAC 2011)

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The Reachability Problem for Petri Nets is Not Elementary

Petri nets, also known as vector addition systems, are a long established model of concurrency with extensive applications in modelling and analysis of hardware, software and database systems, as well as chemical, biological and business processes. The central algorithmic problem for Petri nets is reachability: whether from the given initial configuration there exists a sequence of valid execution steps that reaches the given final configuration. The complexity of the problem has remained unsettled since the 1960s, and it is one of the most prominent open questions in the theory of verification. Decidability was proved by Mayr in his seminal STOC 1981 work, and the currently best published upper bound is non-primitive recursive Ackermannian of Leroux and Schmitz from LICS 2019. We establish a non-elementary lower bound, i.e. that the reachability problem needs a tower of exponentials of time and space. Until this work, the best lower bound has been exponential space, due to Lipton in 1976. The new lower bound is a major breakthrough for several reasons. Firstly, it shows that the reachability problem is much harder than the coverability (i.e., state reachability) problem, which is also ubiquitous but has been known to be complete for exponential space since the late 1970s. Secondly, it implies that a plethora of problems from formal languages, logic, concurrent systems, process calculi and other areas, that are known to admit reductions from the Petri nets reachability problem, are also not elementary. Thirdly, it makes obsolete the currently best lower bounds for the reachability problems for two key extensions of Petri nets: with branching and with a pushdown stack.Comment: Final version of STOC'1

First Steps Towards a Geometry of Computation

We introduce a geometrical setting which seems promising for the study of computation in multiset rewriting systems, but could also be applied to register machines and other models of computation. This approach will be applied here to membrane systems (also known as P systems) without dynamical membrane creation. We discuss the role of maximum parallelism and further simplify our model by considering only one membrane and sequential application of rules, thereby arriving at asynchronous multiset rewriting systems (AMR systems). Considering only one membrane is no restriction, as each static membrane system has an equivalent AMR system. It is further shown that AMR systems without a priority relation on the rules are equivalent to Petri Nets. For these systems we introduce the notion of asymptotically exact computation, which allows for stochastic appearance checking in a priori bounded (for some complexity measure) computations. The geometrical analogy in the lattice Nd0 ; d 2 N, is developed, in which a computation corresponds to a trajectory of a random walk on the directed graph induced by the possible rule applications. Eventually this leads to symbolic dynamics on the partition generated by shifted positive cones C+ p , p 2 Nd0 , which are associated with the rewriting rules, and their intersections. Complexity measures are introduced and we consider non-halting, loop-free computations and the conditions imposed on the rewriting rules. Eventually, two models of information processing, control by demand and control by availability are discussed and we end with a discussion of possible future developments

Threshold nets and cell-assemblies

Motivated by the cell-assemblies theory of the brain, we propose a new formal model of threshold nets (TN). TN are patterned after Petri nets, with a very different firing rule, which removes all tokens upon firing of a transition. The generative power of threshold nets, with and without inhibition, is compared with traditional families of languages. Excitatory TN languages are included by the noncounting regular languages and form an infinite hierarchy for increasing values of threshold. Inhibitory nets are included by the context-sensitive languages. Two new net operators, motivated by the phenomena of growth, learning and brain damage are introduced and compared with Boolean operators

Implementing a distributed lecture-on-demand multimedia presentation system

[[abstract]]Lecture-on-demand (LOD) multimedia presentation technologies in networks are most often used in communication services. Examples of those applications include video-on demand, interactive TV and communication tools in a distance learning system, etc. In this paper, we describe how to present different multimedia objects on a Web-based presentation system. The distributed approach is based on an extended timed Petri net model. Using characterization of extended media streaming technologies, we developed a Web-based multimedia presentation system. For a real-world example, suppose a well-known teacher is giving a lecture/presentation to his students. Because of time constraints and other commitments, many students cannot attend the presentation. The main goal of our system is to provide a feasible method to record and represent a lecture/presentation. Using a browser with windows media services allows those students to view live video of the teacher giving his speech, along with synchronized images of his presentation slides and all the annotations/comments. In our experience, this approach is sufficient for distance learning environments.[[notice]]補正完畢[[conferencetype]]國際[[conferencedate]]20020702~20020705[[conferencelocation]]Vienna, Austri

Using the floor control mechanism in distributed multimedia presentation system

[[abstract]]Establishing a Web-based distributed multimedia presentation system environment is technical challenge. In this paper, we describe how to present different multimedia objects indispensably on a Web presentation system with a floor control mechanism, to be used in a distance learning environment. The distributed approach is based on an extended timed Petri net model. Using the characterization of extended timed Petri nets, we express the temporal behavior of multimedia objects. Then we introduce the concepts of user interaction. The main goal of our system is to provide a feasible method to represent a schedule and navigate different multimedia objects with user interaction. In addition, users can dynamically modify and verify different kinds of conditions during the presentation. To verify the structural mechanism, we implement an algorithm using the Petri net diagram, analyzing the model by a time schedule of multimedia objects, and we produce a synchronous set of multimedia objects with respect to the time duration. In particular, we consider the interactive facilities needed to support the distance learning requirements. We propose a floor control mechanism which provides four types of control (free access, equal control, group discussion and direct contact). These control mechanisms are sufficient for use in a distance learning environment[[notice]]補正完畢[[conferencetype]]國際[[conferencedate]]20010416~20010416[[conferencelocation]]Mesa, United State