Abstract: Quantum mechanical Hamiltonian models of Turing machines are constructed here on a finite lattice of spin-\textonehalf{} systems. The models do not dissipate any energy and they operate at the quantum limit in that the system (energy uncertainty)/(computation speed) is close to the limit given by the time-energy uncertainty principle.

Abstract: The notion algebraic theory was introduced by Lawvere in 1963 (cf. S. Eilenberg and J. B. Wright, Automata in general algebras, Information and Control 11 (1967) 4) to study equationally definable classes of algebras from a more intrinsic point of view. We make use of it to study Turing machines and machines with a similar kind of control at a level of abstraction which disregards the nature of ‘storage’ or ‘external memory’.

Abstract: Work done before on the construction of quantum mechanical Hamiltonian models of Turing machines and general discrete processes is extended here to include processes which erase their own histories. The models consist of three phases: the forward process phase in which a mapT is iterated and a history of iterations is generated, a copy phase, which is activated if and only ifT reaches a fix point, and an erase phase, which erases the iteration history, undoes the iterations ofT, and recovers the initial state except for the copy system. A ballast system is used to stop the evolution at the desired state. The general model so constructed is applied to Turing machines. The main changes are that the system undergoing the evolution corresponding toT iterations becomes three systems corresponding to the internal machine, the computation tape, and computation head. Also the copy phase becomes more complex since it is desired that this correspond also to a copying Turing machine.

Abstract: This paper proposes a welcome hypothesis: a computationally simple device is sufficient for processing natural language. Traditionally it has been argued that processing natural language syntax requires very powerful machinery. Many engineers have come to this rather grim conclusion; almost all working parsers are actually Turing Machines (TM). For example, Woods specifically designed his Augmented Transition Networks (ATN''s) to be Turing Equivalent. If the problem is really as hard as it appears, then the only solution is to grin and bear it. Our own position is that parsing acceptable sentences is simpler because there are constraints on human performance that drastically reduce the computational requirements (time and space bounds). Although ideal linguistic competence is very complex, this observation may not apply directly to a real processing problem such as parsing. By including performance factors, it is possible to simplify the computation. We will propose two performance limitations, bounded memory and deterministic control, which have been incorporated in a new parser YAP.

Abstract: We investigate the complexity of derivations from logic programs, and find it closely related to the complexity of computations of alternating Turing machines. In particular, we define three complexity measures over logic programs—goal-size, length, and depth—and show that goal-size is linearly related to alternating space, the product of length and goal-size is linearly related to alternating tree-size, and the product of depth and goal-size is linearly related to alternating time. The bounds obtained are simultaneous. As an application, we obtain a syntactic characterization of Nondeterministic Linear Space and Alternating Linear Space via logic programs.

Abstract: Let k be a constant -&-ge; 2, and let us consider only deterministic k-tape Turing machines. We assume t2(n) -&-gt; n and t2 is computable in time t2. Then there is a language which is accepted in time t2, but not accepted in any time t1 with t1(n) -&-equil; o(t2(n)). Furthermore, we obtain a strong hierarchy (isomorphic to the rationals Q) for languages accepted in fixed space and variable time.

Abstract: On-line simulation of real-time (k + 1)-tape Turing machines by k-tape Turing machines requires time n(log n)1/(k+1)

Abstract: On-line simulation of real-time (k+1)-tape Turing machines by k-tape Turing machines requires time n(log n)1/(k+1).

Abstract: Several properties of two-dimensional alternating Turing machines are investigated. The first part of this paper investigates the relationship between the classes of sets accepted by space-bounded and finitely leaf-size bounded three-way two-dimensional alternating Turing machines and the classes of sets which are finite intersections of sets accepted by space-bounded three-way two-dimensional nondeterministic Turing machines. The second part of this paper investigates the accepting power and closure properties (under Boolean operations) of two-dimensional alternating Turing machines with only universal states.

Abstract: Procedure calls and messages are two software communication techniques in wide use today. Whereas the semantics of the procedure call are well-known, the newness and variety of message communication make it less understood. Furthermore, the terms \"procedure calls\" and \"messages\" are often used in a general and imprecise manner, and therefore the differences between them tend to blur. This happens, for example, when the claim is made that messages can be programmed using procedure calls-a claim that is both true and, in fact, reflects what is often done in practice. However, this line of reasoning suggests that there is no difference between procedure calls and messages, simply because both can be programmed with a Turing Machine. This is not the point. If precise syntax and semantics are attributed to both procedure calls and messages, then a reasonable comparison can be made and significant differences between these software communications mechanisms do arise. In other words, if both procedure calls and messages are available, how does a user perceive their differences and similarities? The syntax and semantics of the procedure call are a function of the language being used. In this article, the precise semantics of the PL/I procedure call are used because PL/I is typical of many other languages, such as Algol, Fortran, and Ada. Also, in PL/I additional variations of the procedure call are available (coroutines, tasks, and interrupts), and discussions of these contribute to the understanding of the comparison between procedure calls and messages. Choosing precise syntax and semantics for message communication is a more difficult task than it is for a procedure call because there are no standards for messages and the terminology of the subject is not as widely known.

Abstract: The statistical thermodynamics of systems displaying selective behavior is used to discuss some important ultimate physical limitations of computers and biological systems. These cluster around communication of information, measurement, and irreversible processes. The most fundamental limitation is irreducible increase of entropy accompanying selective acts like measurement of preparation. Relevant theory of machines (automata. Turing machines) and issues involved in physical realizations of those machines are discussed. Quantum measurement, the Einstein-Podolsky-Rosen paradox, the fundamental importance of irreversibility, information and entropy, and their relation to Goedel's theorems on completeness and consistency of formal systems are analyzed. Irreversibility of measurement appears necessary to provide quantum mechanics with the incompleteness needed to avoid inconsistency. Motivation and justification of computer paradigms for fundamental modeling of biological systems is given.

Abstract: This paper introduces a two-dimensional alternating Turing machine (2-ATM) which is an extension of an alternating Turing machine to two-dimensions. This paper also introduces a three-way two-dimensional alternating Turing machine (TR2-ATM) which is an alternating version of a three-way two-dimensional Turing machine. We first investigate a relationship between the accepting powers of space-bounded 2-ATM's (or TR2-ATM's) and ordinary space-bounded two-dimensional Turing machines (or three-way two-dimensional Turing machines). We then introduce a simple, natural complexity measure for 2-ATM's (or TR2-ATM's), called -&-ldquo;leaf-size-&-rdquo;, and provides a spectrum of complexity classes based on leaf-size bounded computations. We finally investigate the recognizability of connected patterns by 2-ATM's (or TR2-ATM's).

Abstract: It is proved that the work of an indeterminate m-dimensional Turing machine with time complexity t can be simulated on an indeterminate k-dimensional (k≤m) Turing machine with time complexity t1−(1/m)+(1/k)+ɛ (for any e>0). Moreover, the following generalization to the multidimensional case of the familiar theorem of Hopcroft, Paul, and Valiant is proved: the work of an m-dimensional Turing machine with time complexity t log1/mt [t(n)≥n] can be simulated on an address machine working with time complexity t.

Abstract: A “promise problem” is a formulation of a partial decision problem. Complexity issues about promise problems arise from Even and Yacobi's work in public-key cryptography

Abstract: An induction heating apparatus comprising a static power converter operative to produce high-frequency power from low-frequency power and a heating unit to produce a time-varying magnetic field in response to the high-frequency power. The power converter includes a switching circuit and control means for triggering at high frequency during an incipient stage of operation of the apparatus and lower frequency varying according to the input power to the power converter and the load of the heating unit after the incipient stage.

Abstract: The network approach to computation is more direct and “physical” than the one based on some specific computing devices (like Turing machines). However, the size of a usual—e.g., Boolean—network does not reflect the complexity of computing the corresponding function, since a small network may be very hard to find even if it exists. A history of the work of a particular computing device can be described as a network satisfying some restrictions. The size of this network reflects the complexity of the problem, but the restrictions are usually somewhat arbitrary and even awkward. Causal nets are restricted only by determinism (causality) and locality of interaction. Their geometrical characteristics do reflect computational complexities. And various imaginary computer devices are easy to express in their terms. The elementarily of this concept may help bringing geometrical and algebraic (and maybe even physical) methods into the theory of computations. This hope is supported by the group-theoretical criterion given in this paper for computability from symmetrical initial configurations.

Abstract: An oblivious 1-tape Turing machine can simulate a multicounter machine on-line in linear time and logarithmic space. This leads to a linear cost combinational logic network implementing the first n steps of a multicounter machine and also to a linear time/logarithmic space on-line simulation by an oblivious logarithmic cost RAM. An oblivious log*n-head tape unit can simulate the first n steps of a multicounter machine in real-time, which leads to a linear cost combinational logic network with a constant data rate.

Abstract: Computers and brains are modeled by finite and probabilistic automata, respectively. Probabilistic automata are known to be strictly more powerful than finite automata. The observation that the environment affects behavior of both computer and brain is made. Automata are then modeled in an environment. Theorem 1 shows that useful environmental models are those which are infinite sets. A probabilistic structure is placed on the environment set. Theorem 2 compares the behavior of finite (deterministic) and probabilistic automata in random environments. Several interpretations of Theorem 2 are discussed which offer some insight into some mathematical limits of machine intelligence.

Abstract: Each multicounter machine can be simulated in real-time by an oblivious one-head tape unit.

Abstract: There is given one machine-independent description for a large number of classes of functions, computable on Turing machines with bounded memory and time. Let S and T be classes of nondecreasing functions, satisfying certain simple conditions. It is proved that the class of functions computable on Turing machines with memory bounded by a function from S in time bounded by a function from T coincides with the class of functions obtained from certain simple initial functions by means of explicit transformations, composition, and recursion of the form where s\(\varepsilon \) S, t\(\varepsilon \) T, ¦x¦ is the length of the binary representation of the number x. We also get analogous descriptions of classes of functions computable with bounded memory and classes of functions computable with bounded time.

Abstract: Let H be a language over alphabet Ω and L a language over alphabet Σ, each symbol in Ω being a homomorphism or an anti-homomorphism on L. The set H(L) = {X(w)\Xe.H, WeL} is said to be a bi-language form. In this paper it is shown that the class of language accepted in real time by nondeterministic reversal-bounded multitape Turing machines, NP and the class of the recursively enumerable sets are closed under bi-language form operations when the homomorphisms are linear-erasing, polynomial-erasing and arbitrary respectively.

Abstract: The investigation of how individual preference orderings might be used to construct a social ordering acceptable to the individuals came to a premature end with the discovery of Arrow's impossibility theorem. An extensive body of literature has subsequently been addressed to „suitable” modifications of Arrow's axiom system. A different approach would have been to investigate the question „What means acceptable?”. In the following we propose an exact procedure for the aggregation of preferences under the majority principle. We then discuss briefly an attempt in the literature to interpret impossibility problems like Arrow's as consequences of the unsolvability of the stop-problem of Turing machines. Finally, we give an introduction into the theory of abstract Finite automata with preference-a new approach to the problem of preference aggregation.

Abstract: An oblivious 1-tape Turing machine can on-line simulate a multicounter machine in linear time and logarithmic space. This leads to a linear cost combinational logic network implementing the first n steps of a multicounter machine and also to a linear time/logarithmic space on-line simulation by an oblivious logarithmic cost RAM. An oblivious log *n-head tape unit can simulate the first n steps of a multicounter machine in real-time, which leads to a linear cost combinational logic network with a constant data rate.

Abstract: We introduce a programming language IND that generalizes alternating Turing machines to arbitrary first-order structures. We show that IND programs (respectively, everywhere-halting IND programs, loop-free IND programs) accept precisely the inductively definable (respectively, hyperelementary, elementary) relations. We give several examples showing how the language provides a robust and computational approach to the theory of first-order inductive definability. We then show: (1) on all acceptable structures (in the sense of Moschovakis), r.e. Dynamic Logic is more expressive than finite-test Dynamic Logic. This refines a separation result of Meyer and Parikh; (2) IND provides a natural query language for the set of fixpoint queries over a relational database, answering a question of Chandra and Harel.

Abstract: This paper studies two aspects of the power of space-bounded probabilistic Turing machines. Section 2 presents a simple alternative proof of Simon's recent result [13] that space-bounded probabilistic complexity classes are closed under complement. Section 3 demonstrates that any language in the log n space hierarchy can be recognized by an log n space-bounded probabilistic Turing machine with small error; this is a generalization of Gill's result that any language in NSPACE(log n) can be recognized by such a machine The second result raises interesting questions about space hierarchies, which are considered in section 4. The usual definition is in terms of space-bounded alternating Turing machines with a constant number of alternations [4].