this paper, in view of the particularly rich variety of algorithmic solutions that have been devised for this problem over the past two decades or so, which made it susceptible to some degrees of unification and systematization of independent and general interest. Our discussion starts with the exposition of two basic approaches to LCS computation, due respectively to Hirschberg [1978] and Hunt and Szymanski [1977]. We then discuss faster implementations of this second paradigm, and the data strucures that support them. In Section 5. we discuss algorithms that use only linear space to compute an LCS and yet do not necessarily take \Theta(nm) time. One, final, such algorithm is presented in section 6. where many of the ideas and tools accumulated in the course of our discussion find employment together. In Section 7. we make return to string editing in its general formulation and discuss some of its efficient solutions within a parallel model of computation.

The theory of powerlists was recently introduced by Jayadev Misra [7]. Powerlists can be used to specify and verify certain parallel algorithms, using a notation similar to functional programming languages. In contrast to sequential languages the powerlist notation has constructs for expressing balanced divisions of lists. We study how Prefix Sum, a fundamental parallel algorithm, can be tailored for efficient execution on hypercubic architectures. Then we derive a strategy for mapping most powerlist functions to efficient programs for hypercubic architectures. Keywords: Program derivation; Parallel algorithms; Functional programming; Programming calculi; Hypercubes; Prefix sum 1 Introduction The field of parallel algorithm design has become a major area of research over the last decade. However, the field has yet to develop a standard language for expressing these algorithms. The Powerlist notation, introduced by Jayadev Misra [7], gives us a succinct representation of a certain clas...

this paper. By introducing an extra termination symbol, which signals that an operand was merely terminated due to its length exceeding some bound, operands can be kept as intervals, representing an imprecise operand. Operands terminated in the ordinary way can be taken to represent exact numbers. The cube modeling a function of two variables, can be generalized to a hypercube modeling a poly-homographic function of n variables. For n = 3 the function is defined as: