Showing papers in "Journal of Computer and System Sciences in 1971"

TL;DR: A problem of maximal storage requirements for a simple flowchart model called the Marked Graph Model, which permits algorithnfic answers to problems which in their model were quite complex to solve, e.g., the termination problem.

TL;DR: The use of two-sided quotients adds insight to the theory of star-free events and permits the derivation of some new properties of these events; in particular, every star- free event has at least one quotient which is either empty or full.

TL;DR: A pair grammar is composed of a pair of grammars whose rules and nonterminals are paired that defines a correspondence between elements of the languages defined by the two Grammars.

TL;DR: It is shown that a real-valued function f(x), defined for strings x over a finite alphabet, is of the form (@bg(x)[email protected]) exp(@d|x|) for constants @b, @c, @d, and the acceptance probability function g for a probabilistic automation, if and only if f is of finite rank.

TL;DR: Both the Cooley-Tukey and Good algorithms are induced by a single functional congruence, the solutions to which define all algorithms of the Fast Fourier Transform type.

TL;DR: Several classes of multihead and auxiliary stack automata are introduced and are used to characterize some tape and time complexity classes of Turing machines.

TL;DR: This paper proposes the foundation for a systematic study of the translation of recursive function definitions into flow charts (often called the removal of recursions), and several notions of translation are presented.

TL;DR: It is shown that the smallest AFL containing a homomorphic replication of a slip AFL is also a Slip AFL, and that the resulting AFL is principal if the original AFL isPrincipal.

TL;DR: In Section 2 an attempt is made to give a regular-like characterization of CFL's, using union, product, and a new operation-symbol iteration, and some "auxiliary" symbols are used.

TL;DR: From semigroup theory it follows that the number of noncounting events of order @?1 is finite and the finite automata accepting such events over a fixed alphabet are homomorphic images of a universal automaton.

TL;DR: This paper presents a model for data graphs which can be used to study structural uniformities in data graphs and algebraically characterize those classes of data graphsWhich can be implemented by ''relative addressing'' and by ''relocatable realizations''.

TL;DR: It is shown that a “linear speedup” can be obtained and that one can construct Turing acceptors to simulate grammars without loss of time.

TL;DR: One- and two-dimensional tessellation structures are defined that have the ability to reproduce any finite pattern (formed from the symbols in A) in the sense of Moore.

TL;DR: It is shown that it is possible to express most properties regularly observed in algorithms in terms of 'partial correctness' (i.e., the property that the final results of the algorithm, if any, satisfy some given input-output relation).

TL;DR: A one-to-one correspondence is established between the class of all equal matrix languages and theclass of finite-turn checking automata, which is provided with a counter in its memory to keep track of the number of turns of the stack-head.

TL;DR: A computational procedure is developed for the control problem and the maximum principle essentially "pops out" in the process.

TL;DR: It is shown that if every set in @?

TL;DR: This note shows that the same construction may be applied to tessellation spaces of any finite dimension.

TL;DR: A formal idealization of the data structures used in many ''list processing'' languages is defined and it is shown that under a natural interpretation, these data structures define exactly the context-free languages of automata theory.

TL;DR: A weakening of Blum's Axioms for abstract computational complexity is introduced in order to take into a better account measures that can be finite even when the computations diverge.

TL;DR: General results about measures and unsolvability are presented and constraints are placed on complexity classes so that they possess identical properties.

TL;DR: In this note, natural reference sets are presented which belong to the complete degrees at each level of the arithmetic hierarchy and provide simple methods of determining the degrees of unsolvability for several well-known problems.

TL;DR: Approximation of a smooth function f on a rectangular domain by a tensor product of splines of degree m is considered and convergence of the approximation to a best approximation as h->0 is shown.

TL;DR: A new proof of the basic theorem of SPL's is offered to make the relationship between size and efficiency more revealing and to show that finitely often efficiency is the price of economy of size.

TL;DR: A classification of computational problems is proposed which may have applications in numerical analysis and utilizes the concept of effective method, which has been employed in treating decidability questions within the field of computable numbers.

TL;DR: The relationship between the structure of autonomous finite automata and their operation-preserving functions is considered and the algorithm for determining operation- Preserving functions of A is given.

TL;DR: Several integer-valued functions of nonnegative matrices are defined and various relations between them are obtained and, where appropriate, related to corresponding concepts in graph theory, to obtain upper bounds on the index of primitivity of a fully indecomposable matrix.

TL;DR: It is proved that, using the definitions of realization of one sequential machine by another which appear to be most widely accepted today, every finite sequential machine is linearly realizable over any field of infinite characteristic and even over some fields of finite characteristic.

TL;DR: It is shown that the class of mappings defined by any finitely encodable abstract family of transducers can be generated from a single language over a 2-letter alphabet by pairs of finite state transductions.