STOC

The difficulty of evaluating integers and polynomials has been studied in various frameworks ranging from the addition-chain approach [5] to integer evaluation to recent efforts aimed at generating polynomials that are hard to evaluate [2,8,10]. Here we ...

We investigate the maximum number C(P) of arguments of P that must be tested in order to compute P, a Boolean function of d Boolean arguments. We present evidence for the general conjecture that C(P)=d whenever P(0^d) @@@@ P(1^d) and P is left invariant ...

The concept of computers such as C.mmp and ILLIAC IV is to achieve computational speed-up by performing several operations simultaneously with parallel processors. This type of computer organization is referred to as a parallel computer. In this paper, ...

The following problem was recently raised by C. William Gear [1]: Let F(x₁,x₂,...,x_n) = Σ_i≤j a'_ijx_ix_j + Σ_i b_ix_i +c be a quadratic form in n variables. We wish to compute the point x^→(0) = (x₁⁽⁰⁾,...,x_n⁽⁰⁾), at which F achieves its minimum, by a series ...

Consider the combinational complexity L(f) of Boolean functions over the basis Ω = {f¦ f:{0,1}² → {0,1}}. A new Method for proving linear lower bounds of size 2n is presented. Combining it with methods presented in [12] and [15], we establish for a ...

Let C⁽ⁿ⁾_k be the Boolean function of n variables that equals one iff the number of arguments equal to one is a multiple of k. It is shown that every Boolean expression for C⁽ⁿ⁾_k, allowing all of the 16 binary connectives, has size exceeding εn log n/log ...

The purpose of this paper is to explore the possibility that purely graph-theoretic reasons may account for the superlinear complexity of wide classes of computational problems. The results are therefore of two kinds: reductions to graph theoretic ...

In [1] and [2] a complexity theory for formal languages and automata was developed. This theory implies most of the previously known results and yields many new results as well. Here we develop an analogous theory for several classes of more practically ...

We consider a generalization, which we call the Shannon switching game on vertices, of a familiar board game called HEX. We show that determining who wins such a game if each player plays perfectly is very hard; in fact, it is as hard as carrying out ...

Several procedures based on (not necessarily regular) resolution for checking whether a formula in CN3 is contradictory are considered. The procedures use various methods of bounding the size of the clauses which are generated. The following results are ...

The motivation for this work comes from two general sources. The first source is the basic open question in complexity theory of whether P equals NP (see [1] and [2]). Our approach is to try to show they are not equal, by trying to show that the set of ...

This paper is about mathematical problems in programming language semantics and their influence on recursive function theory. We define a notion of computability on continuous higher types (for all types) and show its equivalence to effective operators. ...

In this paper we wish to consider the problem of proving assertions about programs that construct and alter data structures. Our method will be to define a suitable assertion language L for data structures, to define a simple programming language L' for ...

Formal language theory deals with a variety of classes of languages. Some of these are abstracting features of languages used for communication (as e.g., natural languages, programming languages or languages used in logic), some of them are abstracting ...

In this paper we give a method for decomposing subclasses of different families of languages, into other possibly smaller families. This method can be used to produce languages not in a family by using known examples of languages not belonging to other ...

We develop intercalation lemmas for the computations of the top-down tree transducers defined by Rounds [15] and Thatcher [17]. These lemmas are used to prove necessary conditions for languages all of whose strings are of exponential length to be tree ...

This paper presents some such results for various families of L languages without interactions (see, e.g., [2] or [9]). We have chosen to investigate L languages (without interactions) because:

(i) they are physically well motivated, see, e.g., [5],

(ii)...

The so-called Chomsky hierarchy [5], consisting of regular, context-free, context-sensitive, and recursively enumerable languages, does not account for many “real world” classes of languages, e.g., programming languages and natural languages [4]. This ...

The definition of “grammar form” introduced in [CG] makes it possible to state and prove results about various types of grammars in a uniform way. Among questions naturally formalizable in this framework are many about the complexity or efficiency of ...

The use of hashing schemes for storing extendible arrays is investigated. It is shown that extendible hashing schemes whose worst-case access behavior is close to optimal must utilize storage inefficiently; conversely, hashing schemes that utilize ...

The analysis of the relation between the structure of a program and the function that it computes requires a decomposition of the program into its components. Traditionally this decomposition has been based on the common division of a program into ...

In [1], Kennedy conjectures that for every n node reducible flow graph, there is a sequence of nodes (with repetitions) of length O(nlogn) such that all acyclic paths are subsequences thereof. Such a sequence would, if it could be found easily, enable ...

The running time or computational complexity of a sequential process is usually determined by summing weights attached to the basic operations from which the process is derived. In practice, however, the complexity is often limited by how efficiently it ...

In this paper a new fixedpoint approach towards the semantics of recursive programs is presented. The fixedpoint defined by a recursive program under this semantics contains, in some sense, the maximal amount of “interesting” information which can be ...

We discuss the problem of generating code for a wide class of machines, restricting ourselves to the computation of expression trees. After defining a broad class of machines and discussing the properties of optimal programs on these machines, we derive ...

The Extended String-to-String Correction Problem [ESSCP] is defined as the problem of determining, for given strings A and B over alphabet V, a minimum-cost sequence S of edit operations such that S(A) = B. The sequence S may make use of the operations: ...

The complexity of a number of fundamental problems in computational geometry is examined and a number of new fast algorithms are presented and analyzed. General methods for obtaining results in geometric complexity are given and upper and lower bounds ...

The purpose of this paper is to present new upper bounds on the complexity of algorithms for testing the primality of a number. The first upper bound is 0(n^1/7); it improves the previously best known bound of 0(n^1/4) due to Pollard [11].

The second ...

Let X = {x₁,...,x_N} and Y = {y₁,...,y_N} be sets of N real numbers. We denote by X + Y the multiset {x_i + y_j; 1 ≤ i, j ≤ N} of size N². Berklekamp has posed the problem of sorting X + Y. Harper, Payne, Savage and Strauss [1] show that N²1og₂N comparisons ...

We consider a graph-theoretic elimination process which is related to performing Gaussian elimination on sparse symmetric and unsymmetric systems of linear equations. We discuss good algorithms for finding elimination orderings, showing that a ...