scholarly journals Set difference operation for regular Petri net languages for the producer/consumer problem with the bounded buffer

2021 ◽  
pp. 94-112
Author(s):  
Vitalii Statkevych
Keyword(s):  
Petri Net ◽  
Finite Automaton ◽  
Regular Expression ◽  
Formal Languages ◽  
Reachability Graph ◽  
Explicit Formulas ◽  
Elimination Method ◽  
Difference Operation ◽  
Consumer Problem ◽  
Synchronization Problems

We consider a Petri net for the producer/consumer problem (one of the classical synchronization problems) with the bounded buffer of size n and the regular formal languages Ln, generated by the net. The objective of this paper is to obtain a regular expression for the set difference of languages Ln \ Lm, n > m. For this purpose, we give the finite automaton which accepts the set difference of mentioned languages, and then we use the state elimination method to obtain the regular expression in the recursive form. The main result is illustrated by the examples. In an appendix, we consider the problem with two producers and two consumers with the bounded buffer of size 1. We give a reachability graph and propose the method for obtaining the regular expression. The explicit formulas are given for the problem with two producers and one consumer and also for the problem with one producer and two consumers.

Model reformulation for conflict-free routing problems using Petri Net and Deterministic Finite Automaton

2015 ◽  
Vol 20 (3) ◽  
pp. 262-269 ◽  
Author(s):  
Ryosuke Nakamura ◽  
Kenji Sawada ◽  
Seiichi Shin ◽  
Kenji Kumagai ◽  
Hisato Yoneda
Keyword(s):  
Petri Net ◽  
Finite Automaton ◽  
Deterministic Finite Automaton ◽  
Routing Problems ◽  
Model Reformulation

scholarly journals Regular Expression Quantifiers — m to n Occurrences

2007 ◽  
Vol 15 (2) ◽  
pp. 53-58 ◽  
Author(s):  
Michał Trybulec
Keyword(s):  
Regular Expression ◽  
Formal Languages ◽  
Explicit Definition ◽  
Special Case

Regular Expression Quantifiers — m to n Occurrences This article includes proofs of several facts that are supplemental to the theorems proved in [10]. Next, it builds upon that theory to extend the framework for proving facts about formal languages in general and regular expression operators in particular. In this article, two quantifiers are defined and their properties are shown: m to n occurrences (or the union of a range of powers) and optional occurrence. Although optional occurrence is a special case of the previous operator (0 to 1 occurrences), it is often defined in regex applications as a separate operator - hence its explicit definition and properties in the article. Notation and terminology were taken from [13].

scholarly journals ON A SUPERCLASS OF A-GRAMMARS

2017 ◽  
Vol 20 (10) ◽  
pp. 102-108
Author(s):  
V.P. Tsvetov
Keyword(s):  
Finite Automaton ◽  
Formal Languages ◽  
Regular Languages ◽  
Finite Alphabet ◽  
Graph Structure ◽  
Graph Grammars ◽  
Deterministic Finite Automaton

In this paper we consider a superclass of automaton grammars that can be represented in terms of paths on graphs. With this approach, we assume that vertices of graph are labeled by symbols of finite alphabet A . We will call such grammars graph-generated grammars or G-grammars. In contrast to the graph grammars that are used to describe graph structure transformations, G-grammars using a graphs as a means of representing formal languages. We will give an algorithm for constructing G-grammar which generate the language recognized by deterministic finite automaton. Moreover, we will show that the class of languages generated by G-grammars is a proper superset of regular languages.

scholarly journals Packet Payload Monitoring for Internet Worm Content Detection Using Deterministic Finite Automaton with Delayed Dictionary Compression

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Divya Selvaraj ◽  
Padmavathi Ganapathi
Keyword(s):  
Finite Automaton ◽  
Regular Expression ◽  
Deterministic Finite Automaton ◽  
Memory Space ◽  
Internet Worm ◽  
Regular Expression Matching ◽  
Monitoring Applications ◽  
Communication Links ◽  
Worm Attacks ◽  
Memory Utilization

Packet content scanning is one of the crucial threats to network security and network monitoring applications. In monitoring applications, payload of packets in a network is matched against the set of patterns in order to detect attacks like worms, viruses, and protocol definitions. During network transfer, incoming and outgoing packets are monitored in depth to inspect the packet payload. In this paper, the regular expressions that are basically string patterns are analyzed for packet payloads in detecting worms. Then the grouping scheme for regular expression matching is rewritten using Deterministic Finite Automaton (DFA). DFA achieves better processing speed during regular expression matching. DFA requires more memory space for each state. In order to reduce memory utilization, decompression technique is used. Delayed Dictionary Compression (DDC) is applied for achieving better speeds in the communication links. DDC achieves decoding latency during compression of payload packets in the network. Experimental results show that the proposed approach provides better time consumption and memory utilization during detection of Internet worm attacks.

Study on the Automation Method of Regular Expression to Finite Automaton

2010 ◽  
Vol 34-35 ◽  
pp. 1493-1496
Author(s):  
Qiong Cao ◽  
Xian Ying Huang ◽  
Ke Ke Wang ◽  
Jing Yin
Keyword(s):  
Finite Automaton ◽  
Regular Expression

Regular expression was the foundation of advanced language and compiler. It can be recognized by finite automaton. In this paper, combined with operator priority analysis and the rules of regular expression, the table of priority relationship between operators involved in regular expression has be constructed. Based on the table, realized the automatic convert from regular expression to finite automaton, and the program is given. It provided a new reference of regular expression convert to finite automaton.

scholarly journals One Novel and Optimal Deadlock Recovery Policy for Flexible Manufacturing Systems Using Iterative Control Transitions Strategy

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Ter-Chan Row ◽  
Wei-Ming Syu ◽  
Yen-Liang Pan ◽  
Ching-Cheng Wang
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Flexible Manufacturing ◽  
Flexible Manufacturing Systems ◽  
Manufacturing Systems ◽  
Experimental Results ◽  
Reachability Graph ◽  
Sequential Processes ◽  
Iterative Control

This paper focuses on solving deadlock problems of flexible manufacturing systems (FMS) based on Petri nets theory. Precisely, one novel control transition technology is developed to solve FMS deadlock problem. This new proposed technology can not only identify the maximal saturated tokens of idle places in Petri net model (PNM) but also further reserve all original reachable markings whatever they are legal or illegal ones. In other words, once the saturated number of tokens in idle places is identified, the maximal markings of system reachability graph can then be checked. Two classical S3PR (the Systems of Simple Sequential Processes with Resources) examples are used to illustrate the proposed technology. Experimental results indicate that the proposed algorithm of control transition technology seems to be the best one among all existing algorithms.

scholarly journals PATH DECOMPOSITION AND SEMILINEARITY OF PETRI NETS

2009 ◽  
Vol 20 (04) ◽  
pp. 581-596 ◽  
Author(s):  
HSU-CHUN YEN
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Sufficient Conditions ◽  
Formal Languages ◽  
Path Decomposition ◽  
Reachability Sets ◽  
Reachability Set

Semilinearity plays a key role not only in formal languages but also in the study of Petri nets. Although the reachability set of a Petri net may not be semilinear in general, there are a wide variety of subclasses of Petri nets which enjoy having semilinear reachability sets. In this paper, we develop sufficient conditions for Petri nets under which semilinearity is guaranteed. Our approach, based on the idea of path decomposition, can be used for consolidating several existing semilinearity results as well as for deriving new results all under the same framework.

Sign in / Sign up

Export Citation Format

Share Document