Mihalis Yannakakis

Principles and methods of testing finite state machines-a survey

With advanced computer technology, systems are getting larger to fulfill more complicated tasks: however, they are also becoming less reliable. Consequently, testing is an indispensable part of system design and implementation; yet it has proved to be a formidable task for complex systems. This motivates the study of testing finite stare machines to ensure the correct functioning of systems and to discover aspects of their behavior. A finite state machine contains a finite number of states and produces outputs on state transitions after receiving inputs. Finite state machines are widely used to model systems in diverse areas, including sequential circuits, certain types of programs, and, more recently, communication protocols. In a testing problem we have a machine about which we lack some information; we would like to deduce this information by providing a sequence of inputs to the machine and observing the outputs produced. Because of its practical importance and theoretical interest, the problem of testing finite state machines has been studied in different areas and at various times. The earliest published literature on this topic dates back to the 1950s. Activities in the 1960s mid early 1970s were motivated mainly by automata theory and sequential circuit testing. The area seemed to have mostly died down until a few years ago when the testing problem was resurrected and is now being studied anew due to its applications to conformance testing of communication protocols. While some old problems which had been open for decades were resolved recently, new concepts and more intriguing problems from new applications emerge. We review the fundamental problems in testing finite state machines and techniques for solving these problems, tracing progress in the area from its inception to the present and the stare of the art. In addition, we discuss extensions of finite state machines and some other topics related to testing.

Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs

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On the Desirability of Acyclic Database Schemes

A class of database schemes, called acychc, was recently introduced. It is shown that this class has a number of desirable properties. In particular, several desirable properties that have been studied by other researchers m very different terms are all shown to be eqmvalent to acydicity. In addition, several equivalent charactenzauons of the class m terms of graphs and hypergraphs are given, and a smaple algorithm for determining acychclty is presented. Also given are several eqmvalent characterizations of those sets M of multivalued dependencies such that M is the set of muRlvalued dependencies that are the consequences of a given join dependency. Several characterizations for a conflict-free (in the sense of Lien) set of muluvalued dependencies are provided.

Computing the Minimum Fill-In is NP-Complete

We show that the following problem is NP-complete. Given a graph, find the minimum number of edges (fill-in) whose addition makes the graph chordal. This problem arises in the solution of sparse symmetric positive definite systems of linear equations by Gaussian elimination.

How easy is local search

We investigate the complexity of finding locally optimal solutions to NP-hard combinatorial optimization problems. Local optimality arises in the context of local search algorithms, which try to find improved solutions by considering perturbations of the current solution (“neighbors” of that solution). If no neighboring solution is better than the current solution, it is locally optimal. Finding locally optimal solutions is presumably easier than finding optimal solutions. Nevertheless, many popular local search algorithms are based on neighborhood structures for which locally optimal solutions are not known to be computable in polynomial time, either by using the local search algorithms themselves or by taking some indirect route. We define a natural class PLS consisting essentially of those local search problems for which local optimality can be verified in polynomial time, and show that there are complete problems for this class. In particular, finding a partition of a graph that is locally optimal with respect to the well-known Kernighan-Lin algorithm for graph partitioning is PLS-complete, and hence can be accomplished in polynomial time only if local optima can be found in polynomial time for all local search problems in PLS.

The Complexity of Multiterminal Cuts

In the multiterminal cut problem one is given an edge-weighted graph and a subset of the vertices called terminals, and is asked for a minimum weight set of edges that separates each terminal from all the others. When the number

Memory Efficient Algorithms for the Verification of Temporal Properties

k

The complexity of probabilistic verification

of terminals is two, this is simply the mincut, max-flow problem, and can be solved in polynomial time. It is shown that the problem becomes NP-hard as soon as

Shortest paths without a map

k=3

Expressing combinatorial optimization problems by Linear Programs

, but can be solved in polynomial time for planar graphs for any fixed