We consider the dynamic dictionary matching problem. We are given a set of pattern strings (the dictionary) that can change over time; that is, we can insert a new pattern into the dictionary or delete a pattern from it. Moreover, given a text string, we must be able to find all occurrences of any pattern of the dictionary in the text. Let D 0 be the empty dictionary. We present an algorithm that performs any sequence of the following operations in the given time bounds: (1) insert(p; D i01 ): Insert pattern p[1; m] into the dictionary D i01 . D i is the dictionary after the operation. The time complexity is O(m log jD i j). (2) delete(p; D i01 ): Delete pattern p[1; m] from the dictionary D i01 . D i is the dictionary after the operation. The time complexity is O(m log jD i01 j). (3) search(t; D i ): Search text t[1; n] for all occurrences of the patterns of dictionary D i . The time complexity is O((n + tocc) log jD i j), where tocc is the total number of occurrences of patterns i...

This paper presents the New Systolic Language as a general solution to the problem systolic programming. The language provides a simple programming interface for systolic algorithms suitable for di erent hardware platforms and software simulators. The New Systolic Language hides the details and potential systolic data streams. Data ows and systolic cell programs for the co-processor are integrated with host functions, enabling a single le to specify a complete systolic program. 1

: We consider new algorithms for the solution of many dynamic programming recurrences for sequence comparison and for RNA secondary structure prediction. The techniques upon which the algorithms are based e#ectively exploit the physical constraints of the problem to derive more e#cient methods for sequence analysis. 1. INTRODUCTION In this paper we consider algorithms for two problems in sequence analysis. The first problem is sequence alignment, and the second is the prediction of RNA structure. Although the two problems seem quite di#erent from each other, their solutions share a common structure, which can be expressed as a system of dynamic programming recurrence equations. These equations also can be applied to other problems, including text formatting and data storage optimization. We use a number of well motivated assumptions about the problems in order to provide e#cient algorithms. The primary assumption is that of concavity or convexity. The recurrence relations for bo...