STOC

The equivalence problem for Kleene's regular expressions has several effective solutions, all of which are computationally inefficient. In [1], we showed that this inefficiency is an inherent property of the problem by showing that the problem of ...

We investigate the following:

(1) the relationship between the classes of languages accepted by deterministic and nondeterministic polynomial time bounded Turing machines;

(2) the time and tape complexity of many predicates on the regular sets;

(3) the ...

Every deterministic context-free language can be accepted by a deterministic finite delay pda with jumps. Increasing the number of types or occurrences of jumps increases the family of languages accepted with finite delay. Hence the family of ...

Recently there have been several attempts to prove that every set of strings in @@@@ (i.e., recognizable in deterministic polynomial time) can be recognized in deterministic storage (log n)². The methods used in the attempts were based on that of [1], ...

We consider the first-order theory whose language has as nonlogical symbols the constant symbols 0 and 1, the binary relation symbols = and <, the unary function symbol − and the binary function symbol +

This theory of integers under addition is ...

Simple, polynomial-time, heuristic algorithms for finding approximate solutions to various polynomial complete optimization problems are analyzed with respect to their worst case behavior, measured by the ratio of the worst solution value that can be ...

In this paper we will be concerned with portions of roundoff analysis which can be automated. Conditions are given under which proofs of numerical stability can be performed completely automatically and very economically (in particular, in polynomial ...

An inductive proof in mathematics may often be expressed as an algorithm and a proof that the algorithm is correct. Especially when the proof proceeds by cases, a recursive pattern-matching language, such as Hewitt's MATCHLESS, is a felicitous language ...

A Turing machine multiplies on-line if it receives its inputs low order digits first and it produces the k-th output digit before reading in the (k+1)-st inputs. We present a general method for converting any off-line multiplication algorithm which ...

The paper considers the complexity of bilinear forms in a noncommutative ring. The dual of a computation is defined and applied to matrix multiplication and other bilinear forms. It is shown that the dual of an optimal computation gives an optimal ...

Although general theories are beginning to emerge in the area of automata based complexity theory, there are very few general methods or even general problem formulations in the area of arithmetic complexity. In this paper we propose and defend a ...

Many problems in program optimization have been solved by applying a technique called interval analysis to the flow graph of the program. A flow graph which is susceptible to this type of analysis is called reducible. This paper describes an algorithm ...

A programming language for the partial computable functionals is used as the basis for a definition of the computational complexity of functionals (type2 functions). An axiomatic account in the spirit of Blum is then provided. The novel features of this ...

Several of the results that appear in [4] are stated to be true of polynominal time reducibility (≤_p) but are not proved explicitly. We shall prove several of these results with the hope of shedding some light on the “determinism vs. nondeterminism” ...

This paper contains several results yielding pairs of problems which don't help each other's solution, and therefore which may be said to be complex for “different reasons.” Statements are formalized and results proved within Blum complexity theory, ...

We consider the problem of computing the determinant of a matrix of polynomials; we compare two algorithms (expansion by minors and Gaussian elimination), examining each under two models for polynomial computation (dense univariate and totally sparse). ...

An integer greatest common divisor (GCD) algorithm due to Schönhage is generalized to hold in all euclidean domains which possess a fast multiplication algorithm. It is shown that if two N precision elements can be multiplied in O(N log^a N), then their ...

Let {x_i} be a sequence approximating an algebraic number α of degree r, and let [equation], for some rational function @@@@ with integral coefficients. Let M denote the number of multiplications or divisions needed to compute @@@@ and let M¯ denote the ...

Attributed translations are a means of specifying the input-output relation of a language processing device, such as for example the lexical or syntax box of a compiler. Considered as a mathematical object, an attributed translation is a mapping of ...

The paper presents, as far as the author is aware, the first practical general method for constructing LR(k) parsers. It has been used, without computational difficulty, to produce LR(1), LR(2) and LR(3) parsers for grammars of the size of ALGOL.

The search for efficient algorithms for register allocation dates back to the time of the first Fortran compiler for the IBM 704. Since then, many variants of the problem have been considered; depending on two factors: (1) the particular model for ...

Optimal error analysis with respect to a context-free language may be viewed as the evaluation of an algebraic power series. By generalization of the nodal span context-free recognition algorithm, any algebraic power series is computable in O(n³) steps. ...

Interest in the study of sets of trees, tree languages, has led to the definition of finite automata which accept trees [2,11] and transducers which map trees into other trees [7,9,10]. These generalized machines may read treesfinite automata which ...

search In this paper, we explore the use of neighborhood search techniques for finding optimal solutions to the symmetric Traveling Salesman Problem. These techniques have been dramatically successful in obtaining near-optimal solutions to this problem ...

This paper gives an informal presentation of constructions which, when combined, enable one to construct high level programming languages from algebras or, equivalently, from collections of primitive operations on some set (e.g. from the arithmetic, ...

The object of this paper is to study the mechanism of recursion in a simple, LISP-like programming language, where the only mean of iteration is through recursion. The theory of computation developped in Scott [4] provides the framework of our study. We ...

We investigate various control structures to understand their computational complexity and limitations. It is generally felt that GOTO-less programs constructed from the classical primitives are very restrictive; structured programming languages like ...

Trees in an n node forest are to be merged according to instructions in a given sequence, while other instructions in the sequence ask for the lowest common ancestor of pairs of nodes. We show that any sequence of O(n) instructions can be processed “on ...

Let A be a subset of Σ⁺, the free semigroup generated by a finite set Σ. In Σ⁺ we consider congruences satisfying the condition xñy & xεA@@@@yε A

Among all such congruences there is a largest one, and the quotient monoid by this congruence is denoted by ...

A memory may be regarded as a computer with input, output and storage facilities, but with no explicit functional capability. The only possible outputs are permutations of a multiset of its inputs. Thus the natural question to ask of a class of memories ...