is a much greater percentage of what I am supposed to be doing in life

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Abstract not found

This document has been prepared using the L a T E X system. We thank Donald Knuth for T E X, Leslie Lamport for L a T E X, and Jan van der Steen at CWI for online help. Some figures were prepared by John Tromp using the xpic program. The London Mathematical Society kindly gave permission

"Meaning " may be assigned to a string in a context-free language by defining "at-tributes " of the symbols in a derivation tree for that string. The attributes can be de-fined by functions associated with each production in the grammar. This paper examines the implications of this process when some of the attributes are "synthe-sized", i.e., defined solely in terms of attributes of the descendants of the correspond-ing nonterminal symbol, while other attributes are "inherited", i.e., defined in terms of attributes of the ancestors of the nonterminal symbol. An algorithm is given which detects when such semantic rules could possibly lead to circular definition of some attributes. An example is given of a simple programming language defined with both inherited and synthesized attributes, and the method of definition is compared to other techniques for formal specification of semantics which have appeared in the literature. A simple technique for specifying the "meaning " of languages defined by context-free grammars is introduced in Section 1 of this paper, and its basic mathematical properties are investigated in Sections 2 and 3. An example which indicates how the technique can be applied to the formal definition of programming languages i described in Section 4, and finally, Section 5 contains a somewhat biased comparison of the present method to other known techniques for semantic definition. The discussion in this paper is oriented primarily towards programming languages, but the same methods appear to be relevant also in the study of natural anguages. 1. Introduction. Let

The author and his associates have been experimenting for the past several years with a programming language and documentation system called WEB. This paper presents WEB by example, and discusses why the new system appears to be an improvement over previous ones.

Abstract not found

Let G be any n-vertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which finds such a partition A, B, C in O(n) time.

We discuss the kind of writing that's appropriate in a paper submitted to the math department to complete Phase Two of MIT's writing requirement. First, we review the general purpose of the requirement and the specific way of completing it for the math department.

this document This document was typeset using Donald Knuth's T E X program with Leslie Lamport's L