Vector Addition System Reversible Reachability Problem

The reachability problem for vector addition systems is a central problem of net theory. This problem is known to be decidable but the complexity is still unknown. Whereas the problem is EXPSPACE-hard, no elementary upper bounds complexity are known. In this paper we consider the reversible reachability problem. This problem consists to decide if two configurations are reachable one from each other, or equivalently if they are in the same strongly connected component of the reachability graph. We show that this problem is EXPSPACE-complete. As an application of the introduced materials we characterize the reversibility domains of a vector addition system

Model approximation for batch flow shop scheduling with fixed batch sizes

Batch flow shops model systems that process a variety of job types using a fixed infrastructure. This model has applications in several areas including chemical manufacturing, building construction, and assembly lines. Since the throughput of such systems depends, often strongly, on the sequence in which they produce various products, scheduling these systems becomes a problem with very practical consequences. Nevertheless, optimally scheduling these systems is NP-complete. This paper demonstrates that batch flow shops can be represented as a particular kind of heap model in the max-plus algebra. These models are shown to belong to a special class of linear systems that are globally stable over finite input sequences, indicating that information about past states is forgotten in finite time. This fact motivates a new solution method to the scheduling problem by optimally solving scheduling problems on finite-memory approximations of the original system. Error in solutions for these “t-step” approximations is bounded and monotonically improving with increasing model complexity, eventually becoming zero when the complexity of the approximation reaches the complexity of the original system.United States. Department of Homeland Security. Science and Technology Directorate (Contract HSHQDC-13-C-B0052)United States. Air Force Research Laboratory (Contract FA8750-09-2-0219)ATK Thiokol Inc

Invariants and Home Spaces in Transition Systems and Petri Nets

This lecture note focuses on comparing the notions of invariance and home spaces in Transition Systems and more particularly, in Petri Nets. We also describe how linear algebra relates to these basic notions in Computer Science, how it can be used for extracting invariant properties from a parallel system described by a Labeled Transition System in general and a Petri Net in particular. We endeavor to regroup a number of algebraic results dispersed throughout the Petri Nets literature with the addition of new results around the notions of semiflows and generating sets. Examples are given to illustrate how invariants can be handled to prove behavioral properties of a Petri Net. Some additional thoughts on invariants and home spaces will conclude this note.Comment: 83 page

Measurements, Models, Systems and Design

531 s.

Attaining stability in multi-skill workforce scheduling

In this paper, we define a set inequalities that are satisfied by stable multi-skill workforce schedules. In our analysis, a schedule is said to be stable if it does not contain a blocking pair, extending the notion of blocking pair in the Marriage Model of Gale-Shapley. Skill efficiency is chosen as the criterion in the preference structure. The proposed algorithm either constructs a stable multi-skill workforce schedule or decides that no stable schedule exists

Open Markov Processes and Reaction Networks

We define the concept of an `open' Markov process, a continuous-time Markov chain equipped with specified boundary states through which probability can flow in and out of the system. External couplings which fix the probabilities of boundary states induce non-equilibrium steady states characterized by non-zero probability currents flowing through the system. We show that these non-equilibrium steady states minimize a quadratic form which we call `dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.Comment: 140 pages, University of California Riverside PhD Dissertatio

A service-oriented architecture for integrating the modeling and formal verification of genetic regulatory networks

<p>Abstract</p> <p>Background</p> <p>The study of biological networks has led to the development of increasingly large and detailed models. Computer tools are essential for the simulation of the dynamical behavior of the networks from the model. However, as the size of the models grows, it becomes infeasible to manually verify the predictions against experimental data or identify interesting features in a large number of simulation traces. Formal verification based on temporal logic and model checking provides promising methods to automate and scale the analysis of the models. However, a framework that tightly integrates modeling and simulation tools with model checkers is currently missing, on both the conceptual and the implementational level.</p> <p>Results</p> <p>We have developed a generic and modular web service, based on a service-oriented architecture, for integrating the modeling and formal verification of genetic regulatory networks. The architecture has been implemented in the context of the qualitative modeling and simulation tool G<smcaps>NA</smcaps> and the model checkers N<smcaps>U</smcaps>SMV and C<smcaps>ADP</smcaps>. G<smcaps>NA</smcaps> has been extended with a verification module for the specification and checking of biological properties. The verification module also allows the display and visual inspection of the verification results.</p> <p>Conclusions</p> <p>The practical use of the proposed web service is illustrated by means of a scenario involving the analysis of a qualitative model of the carbon starvation response in <it>E. coli</it>. The service-oriented architecture allows modelers to define the model and proceed with the specification and formal verification of the biological properties by means of a unified graphical user interface. This guarantees a transparent access to formal verification technology for modelers of genetic regulatory networks.</p