Peter B. Ladkin

On binary constraint problems

The concepts of binary constraint satisfaction problems can be naturally generalized to the relation algebras of Tarski. The concept of path-consistency plays a central role. Algorithms for path-consistency can be implemented on matrices of relations and on matrices of elements from a relation algebra. We give an example of a 4-by-4 matrix of infinite relations on which on iterative local path-consistency algorithm terminates. We give a class of examples over a fixed finite algebra on which all iterative local algorithms, whether parallel or sequential, must take quadratic time. Specific relation algebras arising from interval constraint problems are also studied: the Interval Algebra, the Point Algebra, and the Containment Algebra.

Effective solution of qualitative interval constraint problems

Abstract We present a fast algorithm for solving qualitative interval constraint problems, which returns solutions of random problems in less than half a second on average, with the hardest problem taking only half a minute on a RISC workstation. This is a surprising result considering the problem is NP-complete. The fast solution time is attributed to the extraordinary pruning power of the path-consistency computation, and to the fact that all our randomly generated interval networks of size ⩾ 14 were found to be inconsistent, which is rapidly detected by a path-consistency computation. While inconsistency is relatively easy to prove, our algorithm also solves large consistent networks with 100 edges. We conclude that our algorithm suffices for solving qualitative interval constraint problems in practice. Other conclusions are that path-consistency reduces the solution search to an almost linear selection of atomic labels and that path-consistency is by itself an excellent consistency heuristic for random networks with fewer than 6 or more than 15 nodes.

Interpreting Message Flow Graphs

We give a semantics for Message Flow Graphs (MFGs), which play the role for interprocess communication that Program Dependence Graphs play for control flow in parallel processes. MFGs have been used to analyse parallel code, and are closely related to Message Sequence Charts and Time Sequence Diagrams in telecommunications systems. Our requirements are firstly, to determine unambiguously exactly what execution traces are specified by an MFG, and secondly, to use a finite-state interpretation. Our methods function for both asynchronous and synchronous communications. From a set of MFGs, we define a transition system of global states, and from that a Büchi automaton by considering safety and liveness properties of the system. In order easily to describe liveness properties, we interpret the traces of the transition system as a model of Manna-Pnueli temporal logic. Finally, we describe the expressive power of MFGs by mimicking an arbitrary Büchi automaton by means of a set of MFGs.

Lazy caching in TLA

Summary. We address the problem, proposed by Gerth, of verifying that a simplified version of the lazy caching algorithm of Afek, Brown, and Merritt is sequentially consistent. We specify the algorithm and sequential consistency in TLA

Fast algebraic methods for interval constraint problems

^+

Static Deadlock Analysis for CSP-Type Communications

, a formal specification language based on TLA (the Temporal Logic of Actions). We then describe how to construct and check a formal TLA correctness proof.

Compile-time analysis of communicating processes

We describe an effective generic method for solving constraint problems, based on Tarski’s relation algebra, using path-consistency as a pruning technique. We investigate the performance of this method on interval constraint problems. Time performance is affected strongly by the path-consistency calculations, which involve the calculation of compositions of relations. We investigate various methods of tuning composition calculations, and also path-consistency computations. Space performance is affected by the branching factor during search. Reducing this branching factor depends on the existence of ‘nice’ subclasses of the constraint domain. Finally, we survey the statistics of consistency properties of interval constraint problems. Problems of up to 500 variables may be solved in expected cubic time. Evidence is presented that the ‘phase transition’ occurs in the range 6 ≤ n.c ≤15, where n is the number of variables, and c is the ratio of non-trivial constraints to possible constraints.

A Symbolic Approach to Interval Constraint Problems

We present two tests for analyzing deadlock for a class of communicating sequential processes. The tests can be used for deadlock detection in parallel and distributed programs at compile time, or for debugging purposes at run time. They can also be used in conjunction with an algorithm we have for constructing valid execution traces for this class.

Simple Reasoning with Time-Dependent Propositions

We present an algorithm for analyzing deadlock and for constructing sequentializations of a class of communicating sequential processes. The algorithm may be used for deadlock detection in parallel and distributed programs at compile time, or for debugging purposes at run time. The algorithm generates a data structure we call the flow graph, which contains all you need to know about the communications between the processes. If the algorithm is used only for debugging, it is not necessary to retain a copy of the flow graph. Both static deadlock analysis and trace generation are linear in the size of the (minimum) flow graph we construct.

From logic to manuals again

We report on a symbolic approach to solving constraint problems, which uses relation algebra. The method gives good results for problems with constraints that are relations on intervals. Problems of up to 500 variables may be solved in expected cubic time. Strong evidence is presented that significant backtracking on random problems occurs only in the range 6 ≤ n.c ≤ 15, for c ≥ 0.5, where n is the number of variables, and c is the ratio of non-trivial constraints to possible constraints in the problem. Space performance of the method is affected by the branching factor during search, and time performance by path-consistency calculations, including the calculation of compositions of relations.