Alfred V. Aho

Efficient string matching: an aid to bibliographic search

This paper describes a simple, efficient algorithm to locate all occurrences of any of a finite number of keywords in a string of text. The algorithm consists of constructing a finite state pattern matching machine from the keywords and then using the pattern matching machine to process the text string in a single pass. Construction of the pattern matching machine takes time proportional to the sum of the lengths of the keywords. The number of state transitions made by the pattern matching machine in processing the text string is independent of the number of keywords. The algorithm has been used to improve the speed of a library bibliographic search program by a factor of 5 to 10.

Universality of data retrieval languages

We consider the question of how powerful a relational query language should be and state two principles that we feel any query language should satisfy. We show that although relational algebra and relational calculus satisfy these principles, there are certain queries involving least fixed points that cannot be expressed by these languages, yet that also satisfy the principles. We then consider various extensions of relational algebra to enable it to answer such queries. Finally, we discuss our extensions to relational algebra in terms of a new programming language oriented model for queries.

The Transitive Reduction of a Directed Graph

We consider economical representations for the path information in a directed graph. A directed graph

Indexed Grammars—An Extension of Context-Free Grammars

G^t

The theory of joins in relational databases

is said to be a transitive reduction of the directed graph G provided that (i)

Algorithms for finding patterns in strings

G^t

Code generation using tree matching and dynamic programming

has a directed path from vertex u to vertex v if and only if G has a directed path from vertex u to vertex v, and (ii) there is no graph with fewer arcs than

Inferring a Tree from Lowest Common Ancestors with an Application to the Optimization of Relational Expressions

G^t

Equivalences among Relational Expressions

satisfying condition (i). Though directed graphs with cycles may have more than one such representation, we select a natural canonical representative as the transitive reduction for such graphs. It is shown that the time complexity of the best algorithm for finding the transitive reduction of a graph is the same as the time to compute the transitive closure of a graph or to perform Boolean matrix multiplication.

Bounds on the Complexity of the Longest Common Subsequence Problem

A new type of grammar for generating formal languages, called an indexed grammar, is presented. An indexed grammar is an extension of a context-free grammar, and the class of languages generated by indexed grammars has closure properties and decidability results similar to those for context-free languages. The class of languages generated by indexed grammars properly includes all context-free languages and is a proper subset of the class of context-sensitive languages. Several subclasses of indexed grammars generate interesting classes of languages.