Retractions in comparing PROLOG semantics

We present an operational model O and a continuation based denotational model D for a uniform variant of PROLOG, including the cut operator. The two semantical definitions make use of higher order transformations Phi and Psi, respectively. We prove O and D equivalent in a novel way by comparing yet another pair of higher order transformations Phi~ and Psi~, that yield Phi and Psi, respectively, by application of a suitable abstraction operator

Continuation semantics for PROLOG with cut

We present a denotational continuation semantics for PROLOG with cut. First a uniform language B is studied, which captures the control flow aspects of PROLOG. The denotational semantics for B is proven equivalent to a transition system based operational semantics. The congruence proof relies on the representation of the operational semantics as a chain of approximations and on a convenient induction principle. Finally, we interpret the abstract language B such that we obtain equivalent denotational and operational models for PROLOG itself

Towards a taxonomy of parallel branch and bound algorithms

In this paper we present a classification of parallel branch and bound algorithms, and elaborate on the consequences of particular parameter settings. The taxonomy is based upon how the algorithms handle the knowledge about the problem instance to be solved, generated during execution. The starting point of the taxonomy is the generally accepted description of the sequential branch and bound algorithm, as presented in, for example, [Mitten 1970] and [Ibaraki 1976a, 1976b, 1977a, 1977b]

Denotational semantics for unguarded recursion: the demonic case

We show that the technique to prove equivalence of operational and denotational cpo based semantics using retractions, as introduced in de Bruin & Vink [1989] for a sequential backtracking language, can be applied to parallel languages as well. We prove equivalence for a uniform language in which procedure calls need not be guarded. The unguardedness is taken care of by giving a semantics in which the nondeterminism is demonic

Another view on the SSS* algorithm

A new version of the SSS* algorithm for searching game trees is presented. This algorithm is built around two recursive procedures. It finds the minimax value of a game tree by first establishing an upper bound to this value and then successively trying in a top down fashion to tighten this bound until the minimax value has been obtained. This approach has several advantages, most notably that the algorithm is more perspicuous. Correctness and several other properties of SSS* can now more easily be proven. As an example we prove Pearl's characterization of the nodes visited by SSS*. Finally the new algorithm is transformed into a practical version, which allows an efficient use of memory

Trends in game tree search

This paper deals with algorithms searching trees generated by two-person, zero-sum games with perfect information. The standard algorithm in this field is alpha-beta. We will discuss this algorithm as well as extensions, like transposition tables, iterative deepening and NegaScout. Special attention is devoted to domain knowledge pertaining to game trees, more specifically to solution trees. The above mentioned algorithms implement depth first search. The alternative is best first search. The best known algorithm in this area is Stockman's SSS*. We treat a variant equivalent to SSS* called SSS-2. These algorithms are provably better than alpha-beta, but it needs a lot of tweaking to show this in practice. A variant of SSS-2, cast in alpha-beta terms, will be discussed which does realize this potential. This algorithm is however still worse than NegaScout. On the other hand, applying a similar idea as the one behind NegaScout to this last SSS version yields the best (sequential) game tree searcher known up till now: MTD(f)

Searching informed game trees

Well-known algorithms for the evaluation of the minimax function in game trees are alpha-beta and SSS*. An improved version of SSS* is SSS-2. All these algorithms don't use any heuristic information on the game tree. In this paper the use of heuristic information is introduced into the alpha-beta and the SSS-2 algorithm. Extended versions of these algorithms are presented. The subset of nodes which is visited during execution of each algorithm is characterised completely

Game tree algorithms and solution trees

In this paper, a theory of game tree algorithms is presented, entirely based upon the concept of solution tree. Two types of solution trees are distinguished: max and min trees. Every game tree algorithm tries to prune nodes as many as possible from the game tree. A cut-off criterion in terms of solution trees will be formulated, which can be used to eliminate nodes from the search without affecting the result. Further, we show that any algorithm actually constructs a superposition of a max and a min solution tree. Finally, we will see, how solution trees and the related cutoff criterion are applied in major game tree algorithms, like alpha-beta and MTD