Symbolic approaches attack the state explosion problem by introducing implicit representations that allow the simultaneous manipulation of large sets of states. The most commonly used representation in this context is the Binary Decision Diagram (BDD). This paper takes the point of view that other structures than BDD's can be useful for representing sets of values, and that combining implicit and explicit representations can be fruitful. It introduces a representation of complex periodic sets of integer values, shows how this representation can be manipulated, and describes its application to the state-space exploration of protocols. Preliminary experimental results indicate that the method can dramatically reduce the resources required for state-space exploration.

/pdf/symbolic-verification-with-periodic-sets-udq9ekem8y.pdf

Integer programming

Symbolic Verification with Periodic Sets

The purpose of this paper is to present some models for the location of public facilities in nodal networks that explicitly maximize social welfare by accounting for price-elastic demand functions. The models presented here are general; yet they are mathematically equivalent to the plant location problem and are therefore amenable to solution procedures developed for the plant location problem. The models presented here distinguish between two institutional environments that reflect the degree of power of the consumer to choose which facility to patronize. If consumers can be assigned arbitrarily to facilities and can be denied service, then the environment is one of public fiat. If consumers must be served at the facility of their choice, then a “serve-allcomers” environment exists. Separate models for each environment are specified, and the relationship between optimal assignments and pricing policies is developed.

https://www.onlinelibrary.wiley.com/doi/pdf/10.1111/j.1538-4632.1975.tb01024.x

The Optimal Nodal Location of Public Facilities With Price‐Sensitive Demand

/pdf/deterministic-methods-for-mixed-integer-nonlinear-2igi0qokng.pdf

Deterministic Methods for Mixed Integer Nonlinear Programming

A significant problem in the application of rule-based expert systems has arisen in the area of re-engineering such systems to support changes in initial requirements. In dynamic performance environments, the rate of change is accelerated and the re-engineering problem becomes significantly more complex. One mechanism to respond to such dynamic changes is to utilize a cultural algorithm (CA). The CA provides self-adaptive capabilities which can generate the information necessary for the expert system to respond dynamically. To illustrate the approach, a fraud detection expert system was embedded inside a CA. To represent a dynamic performance environment, four different application objectives were used. The objectives were characterizing fraudulent claims, nonfraudulent claims, false positive claims, and false negative claims. The results indicate that a culturally enabled expert system can produce the information necessary to respond to dynamic performance environments.

Using cultural algorithms to support re-engineering of rule-based expert systems in dynamic performance environments: a case study in fraud detection

In recent years many of the facets of the problem of producing secondary school schedules have been subject to systematic processing by means of computer-based strategies. One aspect of the problem which does not hitherto seem to have received this kind of attention is the determination of the course load to be assigned to teachers within a school department. This paper presents the results of research into the feasibility of determining an optimal assignment of teachers to courses using an operators research model.

Integer programming

Citations

Symbolic Verification with Periodic Sets

The Optimal Nodal Location of Public Facilities With Price‐Sensitive Demand

Deterministic Methods for Mixed Integer Nonlinear Programming

Using cultural algorithms to support re-engineering of rule-based expert systems in dynamic performance environments: a case study in fraud detection

An operations research approach to the assignment of teachers to courses

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