Showing papers in "Journal of Computer and System Sciences in 1970"

TL;DR: The amount of storage needed to simulate a nondeterministic tape bounded Turingmachine on a deterministic Turing machine is investigated and a specific set is produced, namely the set of all codings of threadable mazes, such that, if there is any set which distinguishes nondeter microscopic complexity classes from deterministic tape complexity classes, then this is one such set.

TL;DR: It is shown here that the weak secondorder theory of two successors is decidable, thus settling a problem of Buchi, and this result is applied to obtain positive solutions to the decision problems for various other theories, e.g., the weaksecond-order theories of order types built up from the finite types.

TL;DR: The concept of generalized sequential machine (gsm) mapping is developed here in its natural extension to trees (or expressions) in the introduction of syntax directed translations and transformations into formallanguage theory.

TL;DR: Ianov's principal results are that there exist algorithms for deciding whether or not, under all interpretations, a given pair of schemas represent the same programs (i.e., are equivalent), and for reducing a schema to an equivalent simple canonical form.

TL;DR: From this result, many well-known families of AFL can be shown to be (full) principal AFL.

TL;DR: Infinite subfamilies of the family consisting of contextsensitive languages, are introduced such that each language of @?"n is defined by a grammar, called a state grammar, that may be thought of as a context-free gramma with states.

TL;DR: It is shown that a time-bounded nondeterministic Turing acceptor need have only two storage tapes and sufficient conditions for these classes to be AFLs.

TL;DR: The essence of various proofs of undecidability are abstracted and wide classes of properties and general conditions on families of languages such that these proofs of Undecidable hold are found.

TL;DR: The cycle rank of G"R is shown to constitute a lower bound to the star height of certain subsets of R, and results are applied to fully characterize the star Height of events consisting of @?

TL;DR: It is shown that for every regular event R of star height n there exists a nondeterministic state graph G whose states correspond to subsets of the set of states Q of the reduced automaton accepting R and whose cycle rank is precisely n.

TL;DR: It is shown that the context sensitive languages and various time and tape complexity classes are equivalent to classes of two-way deterministic balloon automata.

TL;DR: An existence, uniqueness and convergence theorem is obtained employing the modulus of continuity of the first derivative, f_x(x), and under the more explicit assumption of H6lder continuity several other such results are obtained.

TL;DR: An easily applied method based on linear algebra is developed for finding universal Boolean functions having a small number m of arguments and it is shown that this number is asymptotically minimal.

TL;DR: It is shown that any finite pattern can evolve from a given primitive pattern if the neighborhood scope is four or more, and there are finite patterns that cannot evolve from the primitive pattern for the scope-two case.

TL;DR: The role of subclasses of the recursive functions in proving nonexistence of certain numerical methods is considered, and an initial value problem is treated.

TL;DR: The classes of sequences generated by time- and space- restricted multiple counter machines are compared to the corresponding classes generated by similarly restricted multiple tape Turing machines.

TL;DR: The class of semilinear sets is shown to be the least class of sets which contains all of the stratified semil inear sets and is closed under finite intersection.

TL;DR: Conditions are given under which the classes of formal languages defined by non-deterministic ( deterministic) tape-bounded Turing acceptors will be principal AFLs.

TL;DR: It is shown that the finite difference approach to the solution of elliptic equations results in a special case of the coupled difference equations considered, and the invariant imbedding approach yields stable initial value problems.

TL;DR: It is found that the first two classes of errors yield essentially equivalent effects on properties of the automata considered, and that the same is true for the latter two classes (called ''expanding'' errors).

TL;DR: The convergence of the algorithm is proved by a method similar to cutting plane algorithm for convex programs in Banach Spaces by solving a sequence of linear optimal control systems without state space constraints.

TL;DR: It is concluded that, by factorization, linear Fredholm equations can be effectively replaced by nonlinear Volterra equations.

TL;DR: Several different equivalence relations are defined, and their interrelationship and solvability examined both for the class of all program schemes and for each subclass in which the number of registers is at most n.

TL;DR: It is shown that if the closure operation defining a strong reducibility satisfies certain axioms, then the partial ordering of the subrecursive degrees contains dense chains.

TL;DR: Any nondeterministic tape complexity class L(n) such that sup"n"->"~(L(n)/logn))=0 is a subfamily of the two-way nondetergetic pushdown automaton languages.

TL;DR: A new algebraic structure, the R monoid, is associated with a discrete-time, time-invariant linear dynamical system over acommutative ring R, and its properties are investigated.

TL;DR: The partial recursive functions are shown to be computable in uniformly bounded depth and a comparison of the measure with other proposed measures of computational complexity leads to the suggestion of a list of properties to be checked in classifying such measures.

TL;DR: It is shown that certain relations of equivalence among programs and the relation of a program to the functions whose computation it specifies probably obey the law of excluded middle in this system of logic.

TL;DR: A convex programming problem for a functional defined on a Banach space issolved, and necessary conditions are derived in the form of a maximum principle.