scholarly journals Necessary condition for a Petri net model that incorporates resources to produce an event stream from an unknown initial state

2011 ◽  
Author(s):  
L. V. Allen ◽  
D. M. Tilbury
Keyword(s):  
Petri Net ◽  
Necessary Condition ◽  
Initial State ◽  
Event Stream ◽  
Unknown Initial State

scholarly journals Finding Cut-Offs in Leaderless Rendez-Vous Protocols is Easy

2021 ◽  
pp. 42-61
Author(s):  
A. R. Balasubramanian ◽  
Javier Esparza ◽  
Mikhail Raskin
Keyword(s):  
Lower Bounds ◽  
Petri Net ◽  
Special Class ◽  
Upper Bounds ◽  
Initial State ◽  
Reachability Problem ◽  
Final State ◽  
Final Configuration ◽  
Finite State ◽  
State Agents

AbstractIn rendez-vous protocols an arbitrarily large number of indistinguishable finite-state agents interact in pairs. The cut-off problem asks if there exists a number B such that all initial configurations of the protocol with at least B agents in a given initial state can reach a final configuration with all agents in a given final state. In a recent paper [17], Horn and Sangnier prove that the cut-off problem is equivalent to the Petri net reachability problem for protocols with a leader, and in "Image missing" for leaderless protocols. Further, for the special class of symmetric protocols they reduce these bounds to "Image missing" and "Image missing" , respectively. The problem of lowering these upper bounds or finding matching lower bounds is left open. We show that the cut-off problem is "Image missing" -complete for leaderless protocols, "Image missing" -complete for symmetric protocols with a leader, and in "Image missing" for leaderless symmetric protocols, thereby solving all the problems left open in [17].

PROTOCOL SPECIFICATION DESIGN USING AN OBJECT-BASED PETRI NET FORMALISM

1999 ◽  
Vol 09 (01) ◽  
pp. 97-125
Author(s):  
VLADIMIR P. SLIVA ◽  
TADAO MURATA ◽  
SOL M. SHATZ
Keyword(s):  
Petri Net ◽  
Communication Protocols ◽  
Destination Node ◽  
Analysis Method ◽  
Initial State ◽  
Protocol Specification ◽  
Module Analysis ◽  
Software Models ◽  
Object Based

This paper presents a method for modeling of communication protocols using G-Nets — an object-based Petri net formalism. Our approach focuses on specification of one entity in one node at one time, with the analysis that allows consideration of other layers and nodes in addition to module analysis. We extend G-Nets by the notion of timers, which aids the construction of protocol software models. Our method prevents some types of potential deadlocks and livelocks from being introduced into the produced net models. We present certain net synthesis rules to prevent some potential design errors by including error cases in the model. Thus, our node (site) interplay modeling includes cases in which a message may arrive corrupted or can be lost entirely before it would get to its destination node. Also, since our models have deadlock-preserving skeletons, the verification of global deadlock non-existence can be performed on the less complex skeleton rather than on the full G-Net model. Our analysis method discovers some deadlocks plus other unacceptable markings, which do not allow restoration of the initial state. Finding potential livelocks or overspecification is also a part of the analysis.

scholarly journals Island for gravitationally prepared state and pseudo entanglement wedge

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Masamichi Miyaji
Keyword(s):  
Transition Matrix ◽  
Degrees Of Freedom ◽  
Entanglement Entropy ◽  
Initial Boundary ◽  
Necessary Condition ◽  
Initial State ◽  
Boundary Area ◽  
Generalized Entropy ◽  
Fine Grained ◽  
Boundary State

Abstract We consider spacetime initiated by a finite-sized initial boundary as a generalization of the Hartle-Hawking no-boundary state. We study entanglement entropy of matter state prepared by such spacetime. We find that the entanglement entropy for large subregion is given either by the initial state entanglement or the entanglement island, preventing the entropy to grow arbitrarily large. Consequently, the entanglement entropy is always bounded from above by the boundary area of the island, leading to an entropy bound in terms of the island. The island I is located in the analytically continued spacetime, either at the bra or the ket part of the spacetime in Schwinger-Keldysh formalism. The entanglement entropy is given by an average of complex pseudo generalized entropy for each entanglement island. We find a necessary condition of the initial state to be consistent with the strong sub-additivity, which requires that any probe degrees of freedom are thermally entangled with the rest of the system. We then find a large parameter region where the spacetime with finite-sized initial boundary, which does not have the factorization puzzle at leading order, dominates over the Hartle-Hawking no-boundary state or the bra-ket wormhole. Due to the absence of a moment of time reflection symmetry, the island in our setup is a generalization of the entanglement wedge, called pseudo entanglement wedge. In pseudo entanglement wedge reconstruction, we consider reconstructing the bulk matter transition matrix on A ∪ I, from a fine-grained state on A. The bulk transition matrix is given by a thermofield double state with a projection by the initial state. We also provide an AdS/BCFT model by considering EOW branes with corners. We also find the exponential hardness of such reconstruction task using a generalization of Python’s lunch conjecture to pseudo generalized entropy.

Optimal Mode-Switching for Hybrid Systems with Unknown Initial State

2006 ◽  
pp. 95-100 ◽  
Author(s):  
Henrik Axelsson ◽  
Mauro Boccadoro ◽  
Yorai Wardi ◽  
Magnus Egerstedt
Keyword(s):  
Hybrid Systems ◽  
Mode Switching ◽  
Initial State ◽  
Optimal Mode ◽  
Unknown Initial State

OPTIMAL MODE-SWITCHING FOR HYBRID SYSTEMS WITH UNKNOWN INITIAL STATE

2006 ◽  
Vol 39 (5) ◽  
pp. 95-100
Author(s):  
Henrik Axelsson ◽  
Mauro Boccadoro ◽  
Yorai Wardi ◽  
Magnus Egerstedt
Keyword(s):  
Hybrid Systems ◽  
Mode Switching ◽  
Initial State ◽  
Optimal Mode ◽  
Unknown Initial State

Modeling and Solving Product Configuration Problems Using Petri Net

2011 ◽  
Vol 201-203 ◽  
pp. 1379-1383
Author(s):  
Dong Yang
Keyword(s):  
Petri Net ◽  
Mass Customization ◽  
Discrete Systems ◽  
Product Configuration ◽  
Enabling Technology ◽  
Initial State ◽  
Final State ◽  
Structural Relationships ◽  
Configuration Problem

This Product configuration is a key enabling technology for implementing mass customization production. In this paper, we present an approach for modeling product configuration problems using Petri Net, a well-defined formalism for describing complex discrete systems. In the presented approach, components within a configurable product are modeled as places of PN whereas structural relationships between components are represented as transitions of PN. Configuration rules such as inclusion and exclusion rules are also described through the elements of PN. By modeling product configuration as a PN, a configuration solution is a set of transitions leading from the initial state of PN to a final state of PN. Therefore, the configuration problem can be solved by analyzing corresponding PN representation.

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