Showing papers on "Turing machine published in 1981"

Complexity classes and theories of finite models

Abstract: LetL $$ \subseteq $$ Σ* be accepted in timef(n) by a nondeterministic Turing machine. Then there is a monadic existential second-order sentence σ in the language of + such that for everyx∈Σ*,x∈L if and only if a certain structureU of cardinalityf(|x|) satisfies σ. It follows that ifL is accepted in nondeterministic timen d, d a natural number, then there is a sentence whose relational symbols ared-ary or less, whose finite spectrum isL.

Parallel Image Processing by Memory-Augmented Cellular Automata

Abstract: This paper introduces a generalization of cellular automata in which each celi is a tape-bounded Turing machine rather than a finite-state machine. Fast algorithms are given for performing various basic image processing tasks by such automata. It is suggested that this model of parallel computation is a very suitable one for studying the advantages of parallelism in this domain.

Unsolvability of the universal theory of finite groups

Abstract: The following theorem is proved in this article. THEOREM I. The universal theory of finite groups is unsolvable. By the same token, a negative answer to a question of M. I. Kargapolov in "Kourovska Notebook" [i, Question 1.25] is given. The proof is based on ideas and methods of [2-4],the main idea among them beingthe connection between the processing of words in Turing machines and elementary transformations of words in associative calculi. Let us define a two-tape Minsky machine /~ with the internal states ~o,~I ..... ~a and the following working program for it:

New Real-Time Simulations of Multihead Tape Units

Abstract: Single-head tapes are used to simulate multihead Turing machine tape units without loss. For one-dimensional tapes, the new simulations are simpler and use far fewer tapes than prevj known simulations. For multidimensional tapes, the results are entirely new.

Reversal complexity of counter machines

Abstract: It has long been known that deterministic 1-way counter machines recognize exactly all r.e. sets. Here we investigate counter machines with general recursive bounds on counter reversals. Our main result is that for bounds which are at least linear, counter reversal is polynomially related to Turing machine time, for both 1-way and 2-way counter machines and in both the deterministic and the nondeterministic cases. This leads to natural characterizations of the classes P and NP, and hence of the P =? NP question, on the counter machine model. We also establish reversal complexity hierarchies for counter machines, using a variety of techniques which include translation of Turing machine time hierarchies, padding arguments as well as more ad hoc counting arguments.

Relationships between Probabilistic and Deterministic Tape Complexity

Abstract: By giving a matrix inversion algorithm that uses a small amount of space, a result of Simon is improved: For constructible functions f(n)∉ o(logn) f(n) tape-bounded probabilistic Turing machines can be simulated on deterministic ones within (f(n))2 space.

Finite and infinite regular thue systems

Abstract: This dissertation studies certain classes of Thue system, concentrating on the Church-Rosser property. The following new results are obtained about infinite regular Thue systems S: (1) if S is Church-Rosser, the word problem is solvable in linear time; (2) if S is monadic Church-Rosser, it defines a nontrivial boolean algebra of DCFLs; (3) if S is monadic Church-Rosser and so is another system T, equivalence of S and T is decidable; (4) if S is monadic, it is decidable if S is Church-Rosser; (5) if S is not monadic it is undecidable if S is Church-Rosser. The following new results are obtained about finite Thue systems S: (1) it is undecidable if there exists another finite Thue system T which is equivalent to S and is Church-Rosser (respectively: almost confluent, preperfect); (2) it is undecidable if S generates a Church-Rosser congruence. Some of these results generalise results about finite Thue systems, and some answer what had previously been open questions. The results are obtained using the theories of automata and formal languages, of Turing machines, and of finitely presented groups.

Space-bounded probabilistic turing machine complexity classes are closed under complement (Preliminary Version)

Abstract: For tape constructible functions S(n)≥log n, if a language L is accepted by an S(n) tape bounded probabilistic Turing machine, then there is an S(n) tape bounded probabilistic Turing machine that accepts L, the complement of L.

Pure grammars and pure languages

Abstract: The notion of “pure grammar” is introduced as a semi-Thue system with no non-terminals. The basic properties of pure grammars and the “pure languages” that they generate are investigated. Other topics introduced are “definite Turing machines” that accept pure languages, pure parallel languages, pure relations and pure Post canonical systems.

On heads versus tapes

Abstract: 2-dimensional 2-tape Turing machines cannot simulate 2-dimensional Turing machines with 2 heads on 1 tape in real time.

Measures of parallelism in alternating computation trees (Extended Abstract)

Abstract: We examine three ways of restricting the size (and shape) of the accepting computation trees of alternating Turing machines. We continue study by examining bounds on the number of leaves in the tree (Section 3), the 'width' of the tree (Section 4), and the number of nodes at any level of the tree (Section 5). Each of these measures can be interpreted as a limit on the amount of parallelism permitted the computation.

The competence of a multiple context learning system

Abstract: There are four ways in which a finite (and therefore realizable) robot learning system can be given beyond-finile-slutc computational power: (1) by being given “auxiliary” actions, like speech, the system achieves a beyond-finile-stale “competence”(2) by being coupled to (made “open” to) a beyond-finite-statc system, like the real world, the system attains a beyond-finite-state “performance” (3) by being limited to a finite “lifetime”, the system's finite-stale behaviour can be made indistinguishable from beyond-finite-state “competence” and “performance” and (4) by being taught the grammar of a beyond-finite-state language, the system acquires a beyond-finite-state “competence”. The “competence” and “performance” of our Multiple Context Learning System (MCLS) have been argued and demonstrated, previously, in the first three ways, even though our critics choose to ignore the record! Here, it is shown explicitly and in detail how the MCLS can learn, hold and simulate both the finite-stale controller and th...

Space-bounded simulation of multitape turing machines

Abstract: A new proof of a theorem of Hopcroft, Paul, and Valiant is presented: Every deterministic multitape Turing machine of time complexityT(n) can be simulated by a deterministic Turing machine of space complexityT(n)/logT(n). The proof includes an overlap argument.

Simulations among multidimensional turing machines

Abstract: For all d ≥ 1 and all e ≫ d, every deterministic multihead e-dimensional Turing machine of time complexity T(n) can be simulated on-line by a deterministic multihead d-dimensional Turing machine in time O(T(n)1+1/d-1/e(log T(n))O(1)) This simulation almost achieves the known lower bound Ω(T(n)1+1/d-1/e) on the time required Furthermore, there is a deterministic d-dimensional machine with just two worktape heads that simulates the e-dimensional machine on-line in time O(T(n)1+1/d-1/delog T(n)) These simulations are interpreted in terms of dynamic embeddings among data structures

A simplified proof of the real-time recognizability of palindromes on turing machines

Abstract: A comparatively short proof is given of the recognizability of palindromes in real time on multitape Turing machines. It is based on the same idea as the original proof by the author, and on Z. Galil's idea for simplifying the proof by using the Fischer-Paterson algorithm for finding all symmetric suffixes in linear time.

A Survey on Oracle Techniques

Abstract: The paper gives a survey on oracle approaches in nonlinear and combinatorial optimization. We present a formal definition of oracle algorithms in terms of mappings rather than in the framework of Turing machines with query tapes. We discuss the application of oracle techniques in fixed point theory and convex optimization. Using oracle arguments we derive lower bounds on the computational complexity in combinatorial optimization. Finally we examine formally equivalent concepts in contrast to their computational strength.

On the Tranformation of Derivation Graphs to Derivation Trees (Preliminary Report)

Abstract: Derivation graphs of arbitrary grammars are transformed into trees. The transformations are based on the notion of ancestors, mapping subderivations into single nodes. Using the weight and the diameter of these nodes as parameters two new complexity measures on grammars are introduced, which are compared with the time and the space complexity measures of nondeterministic turing machines.

Chomsky-Schützenberger Representations for Families of Languages and Grammatical Types

Abstract: The paper has two parts. In Part I, we shall present Chomsky-Schutzenberger theorems for the families of context-sensitive (CS)and recursive-enumerable (RE) languages.

Stateless Turing Machines and Fixed Points

Abstract: Thes n m function defined in the iteration theorem is shown to be quite subelementary through the use of stateless Turing machines. This means that recursion theorems can be used subrecursively with no change in computational complexity.