Algebraic properties of processes for Local Action Systems

2002 ◽  
Vol 12 (4) ◽  
pp. 423-448
Author(s):  
NICO VERLINDEN ◽  
DIRK JANSSENS
Keyword(s):  
Petri Nets ◽  
Formal Semantics ◽  
Dynamic Structure ◽  
Concurrent Systems ◽  
Local Action ◽  
Graph Rewriting ◽  
Action Systems ◽  
Algebraic Properties ◽  
Dynamic Structures

Graph rewriting has been used extensively to model the behaviour of concurrent systems and to provide a formal semantics for them. In this paper, we investigate processes for Local Action Systems (LAS); LAS generalize several types of graph rewriting based on node replacement and embedding. An important difference between processes for Local Action Systems and the process notions that have been introduced for other systems, for example, Petri nets, is the presence of a component describing the embedding mechanism. The aim of the paper is to develop a methodology for dealing with this embedding mechanism: we introduce a suitable representation (a dynamic structure) for it, and then investigate the algebraic properties of this representation. This leads to a simple characterization of the configurations of a process and to a number of equational laws for dynamic structures. We illustrate the use of these laws by providing an equational proof of one of the basic results for LAS processes, namely that the construction yielding the result graph of a process behaves well with respect to the sequential composition of processes.

An Axiomatic Characterization of a Class of Petri Nets

1991 ◽  
Vol 14 (4) ◽  
pp. 477-491
Author(s):  
Waldemar Korczynski
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Axiomatic Characterization ◽  
Algebraic Characterization

In this paper an algebraic characterization of a class of Petri nets is given. The nets are characterized by a kind of algebras, which can be considered as a generalization of the concept of the case graph of a (marked) Petri net.

Overview

2021 ◽  
pp. 11-26
Author(s):  
Elvira Silva ◽  
Spiro E. Stefanou ◽  
Alfons Oude Lansink
Keyword(s):  
Decision Making ◽  
Transaction Costs ◽  
Capital Stock ◽  
Adjustment Costs ◽  
Dynamic Structure ◽  
Dynamic Decision Making ◽  
Rapid Rate ◽  
Absolute Rate ◽  
Decision Environment

This chapter characterizes production in a dynamic decision-making environment. The classic characterization of static firm decision making is contrasted with the dynamic decision environment where not all inputs are freely adjusted. The latter characterization is motivated by the conjecture that transaction costs are associated with adjusting the capital stock at a rapid rate per unit of time and these costs increase rapidly with the absolute rate of investment. In fact, these costs increase so rapidly that the firm may never attempt to achieve a jump in its capital stock at any given moment. Such transaction (or adjustment) costs have implications for the nature of the technology. This interplay is introduced in this chapter and serves as a foundation for the dynamic structure that follows throughout the book.

scholarly journals DOUBLE CROSSED PRODUCTS OF LOCALLY COMPACT QUANTUM GROUPS

2005 ◽  
Vol 4 (1) ◽  
pp. 135-173 ◽  
Author(s):  
Saad Baaj ◽  
Stefaan Vaes
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Matched Pair ◽  
Crossed Products ◽  
Locally Compact ◽  
Locally Compact Quantum Groups ◽  
Algebraic Properties ◽  
Locally Compact Quantum Group ◽  
Compact Quantum Groups

For a matched pair of locally compact quantum groups, we construct the double crossed product as a locally compact quantum group. This construction generalizes Drinfeld’s quantum double construction. We study the modular theory and the $\mathrm{C}^*$-algebraic properties of these double crossed products, as well as several links between double crossed products and bicrossed products. In an appendix, we study the Radon–Nikodym derivative of a weight under a quantum group action (following Yamanouchi) and obtain, as a corollary, a new characterization of closed quantum subgroups. AMS 2000 Mathematics subject classification: Primary 46L89. Secondary 46L65

Observations of the dynamic structure of snow avalanches

1993 ◽  
Vol 18 ◽  
pp. 313-316 ◽  
Author(s):  
K. Nishimura ◽  
N. Maeno ◽  
F. Sandersen ◽  
K. Kristensen ◽  
H. Norem ◽  
...  
Keyword(s):  
Dynamic Structure ◽  
Velocity Shear ◽  
Sensor Data ◽  
Video Tape ◽  
Snow Avalanches ◽  
Western Norway ◽  
Wet Snow ◽  
Avalanche Flow ◽  
Dynamic Structures ◽  
Internal Velocity

During two winters, 1990–92, the dynamic structures of snow avalanches were studied in western Norway. Artificially released wet-snow avalanches ran down the avalanche chute and stopped in front of the retaining dam. Running velocity distributions were obtained not only by video tape recorder, but also by various other recording instruments. Internal velocity was derived for the last avalanche by frequency analysis of impact pressure and optical sensor data. The vertical velocity shear of the avalanche flow has been estimated to be in the range 1–10 s−1.

scholarly journals Formal and Executable Specification of Random Waypoint Mobility Model Using Timed Coloured Petri Nets for WMN

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Naeem Akhtar Khan ◽  
Farooq Ahmad ◽  
Sher Afzal Khan
Keyword(s):  
Petri Nets ◽  
Formal Model ◽  
Formal Semantics ◽  
Cost Effective ◽  
Mobility Model ◽  
Mesh Network ◽  
Coloured Petri Nets ◽  
Border Effect ◽  
Cost Effective Alternative ◽  
Random Waypoint

The wireless mesh network (WMN) is an emerging and cost-effective alternative paradigm for the next generation wireless networks in many diverse applications. In the performance evaluation of routing protocol for the WMN, it is essential that it should be evaluated under realistic conditions. The usefulness of specific mobility protocol can be determined by selection of mobility model. This paper introduces a coloured Petri nets (CP-nets) based formal model for implementation, simulation, and analysis of most widely used random waypoint (RWP) mobility model for WMNs. The formal semantics of hierarchical timed CP-nets allow us to investigate the terminating behavior of the transitions using state space analysis techniques. The proposed implementation improves the RWP mobility model by removing the “border effect” and resolves the “speed decay” problem.

WATSON-CRICK BORDERED WORDS AND THEIR SYNTACTIC MONOID

2008 ◽  
Vol 19 (05) ◽  
pp. 1163-1179 ◽  
Author(s):  
LILA KARI ◽  
KALPANA MAHALINGAM
Keyword(s):  
Dna Computing ◽  
Complete Characterization ◽  
Syntactic Monoid ◽  
Algebraic Properties ◽  
Dna Strands ◽  
Single String ◽  
Mathematical Formalization

DNA strands that, mathematically speaking, are finite strings over the alphabet {A, G, C, T} are used in DNA computing to encode information. Due to the fact that A is Watson-Crick complementary to T and G to C, DNA single strands that are Watson-Crick complementary can bind to each other or to themselves in either intended or unintended ways. One of the structures that is usually undesirable for biocomputation, since it makes the affected DNA string unavailable for future interactions, is the hairpin: If some subsequences of a DNA single string are complementary to each other, the string will bind to itself forming a hairpin-like structure. This paper studies a mathematical formalization of a particular case of hairpins, the Watson-Crick bordered words. A Watson-Crick bordered word is a word with the property that it has a prefix that is Watson-Crick complementary to its suffix. We namely study algebraic properties of Watson-Crick bordered and unbordered words. We also give a complete characterization of the syntactic monoid of the language consisting of all Watson-Crick bordered words over a given alphabet. Our results hold for the more general case where the Watson-Crick complement function is replaced by an arbitrary antimorphic involution.

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