Showing papers in "Theory of Computing Systems \/ Mathematical Systems Theory in 1977"

Local maps inducing surjective global maps of one-dimensional tessellation automata

Abstract: In this paper, we investigate some combinatorial aspects ofC-surjective local maps, i.e., local maps inducing surjective global maps,CF-surjective local maps, i.e., local maps inducing surjective restrictions of global maps on the setCF of finite configurations, andC-injective local maps, i.e., local maps inducing injective local maps, of one-dimensional tessellation automata.

On jump-deterministic pushdown automata

Abstract: The realtime one-state deterministic pushdown automata with jumps define the family of deterministic languages. A simplified regularity test for deterministic languages can be derived from this fact.

On random nonlinear contractions

Abstract: A fixed point theorem for random nonlinear contraction mappings is proven. The random nonlinear contraction principle is then used to study the existence and uniqueness of solutions for a class of random nonlinear integral equations.

Inclusion complete tally languages and the Hartmanis-Berman conjecture

Abstract: Stimulated by the work of Hartmanis and Berman [5], we study the question of the existence of a tally languageL inNP such thatL is inP if and only ifP = NP. The method used is applicable to questions regarding the comparison of a wide range of pairs of classes of formal languages specified by machines whose computational resources are bounded in time or space.

Non-prinicipalité du cylindre des langages à compteur

Abstract: Le cylindre des langages a compteur n'est pas principal Ce resultat n'apporte cependant pas la reponse entiere a la conjecture de S. Greibach [8] sur l'AFDL des langages a compteur, mais reduit le probleme a montrer que notre hierarchie en reste une vis a vis de l'operation de “gsm mapping” inverse.

The cartesian composition of automata

Abstract: There are several known ways to define a product automaton on the cartesian product of the state sets of two given automata. This paper introduces a new product called the cartesian composition and discusses how various properties of the product automaton depend on the corresponding properties of the factors. A main result is that any finite connected automaton has a unique representation as a cartesian composition of prime automata.

Measure-preserving homeomorphisms of the torus represent all finite entropy ergodic transformations

Abstract: We show that every finite entropy ergodic transformation can be represented as a Lebesgue measure-preserving homeomorphism of the twodimensional torus. Whether this is possible with diffeomorphisms is still unknown. Our proof suggests a notion of “universality” for homeomorphisms, about which we formulate several natural but unanswered questions.

A model for pattern perception with musical applications part I: Pitch structures as order-preserving maps

Abstract: The initial five papers of this series on pattern perception treat first, the perception of pitch in musical contexts and then, the perception of timbre and speech. Each sound is considered to be embedded in a “context” consisting of those sounds which surround it or coincide with it. The apprehension of a musical pattern depends upon the perceptibility of certain relations between, and properties of, its parts (e.g. “motifA is similar to motifB“ or “G is the tonic”). It is hypothesized that, because of the limitations of short term memory, the perception of specific relations and properties requires that certain “mental reference frames” be extracted from the various contexts. However, a reference frame which supports the perception of any specified relation may be extracted from only very few of all possible contexts. The choices of musical materials in both Western and non-Western music are shown to avoid precisely such difficulties. When they are not avoided, distortions of perception are predicted and methods for experimental verification are suggested. This theory is then applied to suggest new materials for the composition of both “microtonal” and “tonecolor” music. This is done in a manner which exposes the correspondence between each choice of musical materials and those musical properties and relations whose perception is (or is not) thereby supported.

Le cylindre des langages linéaires

Abstract: Define a cylinder to be a family of languages which is closed under inverse homomorphisms and intersection with regular sets. A number of well-known families of languages are cylinders: —CFL, the family of context-free languages, is a principal cylinder, i.e. the smallest cylinder containing a languageLO described in [6]. —the family of deterministic context-free languages is proved to be a nonprincipal cylinder in [7]. —the family of unambiguous context-free languages is a cylinder: to prove that it is not principal seems to be a very hard problem.

The Complexity of Monotone Boolean Functions

Abstract: We study the realization of monotone Boolean functions by networks. Our main result is a precise version of the following statement: the complexity of realizing a monotone Boolean function ofn arguments is less by the factor (2/πn)1/2, whereπ is the circular ratio, than the complexity of realizing an arbitrary Boolean function ofn arguments. The proof combines known results concerning monotone Boolean functions with new methods relating the computing abilities of networks and machines.

One dimensional-two phase particulate flow

Abstract: A computer model, originally developed by Crowe at Washington State University, which predicts the velocity of solid particles entrained in a one-dimensional gas stream, is modified to improve its accuracy and extend the range of velocity prediction. The program is also used to demonstrate the effects that initial particle velocity and particle concentration have on velocity predictions. The accuracy of the model is confirmed by comparing the theoretical predictions with experimentally measured velocities of particles varying in size, shape and density. For all cases where test data could be measured accurately, the theoretical predictions are shown to be in good agreement with the average experimental values.

The lattice of minimal realizations of response maps over rings

Abstract: A lattice characterization is given for the class of minimal-rank realizations of a linear response map defined over a (commutative) Noetherian integral domain. As a corollary, it is proved that there are only finitely many nonisomorphic minimal-rank realizations of a response map over the integers, while for delay-differential systems these are classified by a lattice of subspaces of a finite-dimensional real vector space.

Approximation by bernstein systems

Abstract: LetK denote an arbitrary compact subset of realL 2. Letf be any causal continuous function onL 2. Then there is a linear differential system:z(t)=A(t)z(t)+B(t)u(t), and a memoryless polynomic state to output mapw(t)=φ(z(t),t) such that the system, $$\hat f$$ , thereby computed satisfies $$\mathop {\sup }\limits_{u \in K} ||f(u) - \hat f(u)||< \varepsilon$$ wheree >0 is arbitrary. This and other results are developed.

Real-time recognition of substring repetition and reversal

Abstract: Real-time multitape Turing machine algorithms are presented for recognizing the languages {wxyxz∈Σ*:|w|=r|x,|z| =t|x|} and {wxyxRz∈Σ*:|w|=r|x,|z| =t|x|} for fixedr, s, andt and for string-matching with “forced mismatches”

Fault Diagnosis of Semiconductor Random Access Memories.

Abstract: : This report deals with the problems of testing semiconductor random access memories and of locating faults on a memory board. Memory test procedures can be divided into three classes, functional testing, pattern sensitivity testing and DC parametric testing. Existing test procedures for testing semiconductor memories are either limited in their fault coverage or require a prohibitive amount of time. A new functional test procedure based on a fault model that takes into account a large variety of faults encountered with semiconductor memories is presented. The fault model is not based on the 'gate' level as in classical fault diagnosis but is formulated on a higher level in terms of functional blocks, like the decoder and the memory cell array. The proposed functional test procedure takes 0(n x log sub 2) units of time where n is the number of words in memory. This gives a dramatic improvement in the testing time required over well-known test procedures line 'galpat' and 'Walking Ones' which take 0(n squared) units of time. Algorithms for the functional test procedure are given. The problem of locating faults on a memory board to memory chips, decoder logic, data registers, and bussing structure is discussed. A test scheme for this problem is given. Finally various test procedures presented in the thesis are evaluated for fault coverage, time requirement and east of implementation.

A model for pattern perception with musical applications part II: The information content of pitch structures

Abstract: This is the second paper of a series which begins by treating the perception of pitch relations in musical contexts and the perception of timbre and speech. The first paper discusses in some detail those properties of musical scales required in order for them to function as “reference frames” which provide for the “measurement” of intervals such that ([1], p. 270),Every melodic phrase, every chord, which can be executed at any pitch, can be also executed at any other pitch in such a way that we immediately perceive the characteristic marks of their similarity. Here we continue this discussion by developing quantitative measures of the degree to which different scales possess the above properties. Then that property of musical scales which permits a listener to code the pitches of which it is constituted into “degrees” is examined and a corresponding quantitative measure developed. Musical scales are shown to be optimal choices with respect to both the former and latter measures, and a theory limiting those scales which are musically useful to a small fraction of possible sets of pitches is proposed. Existing scales which have been examined fall within the theory, which links the techniques of composition which may be used (i.e., those which produce perceptible relations between musical segments) to the above properties of the scale structures. This paper is not self-contained—reading of the previous paper in this series is required.

Simple context-free languages and free monadic recursion schemes

Abstract: A context-free language is said to be simple if it is accepted by a single-state deterministic pushdown store acceptor that operates in real-time and accepts by empty store. While the problem remains open of deciding whether or not the language accepted by a deterministic pushdown store acceptor is simple, it is shown that this problem is equivalent to another problem in schemata theory. This question is that of determining whether or not a monadic recursion scheme has a strongly equivalent free scheme.

Representation of a word function as the sum of two functions

Abstract: We establish an algebraic condition which is necessary and sufficient for a word function of finite rank to be expressible as the sum of two functions, each of rank lower than that of the given function.

Investigation of heat transfer in straight and curved rectangular ducts using liquid crystals thermography

Abstract: : A rectangular cross section channel with both straight and curved test sections was used to investigate the effect of Taylor-Goertler vortices on the heat transfer from the curved section by comparing the results with those obtained in the straight section. The flow was heated through the Joulean heating of one of the walls which was made of Temsheet. Liquid crystals were applied on the surfaces of both test sections. Experiments were run for several values of the volumetric flow rate corresponding to Reynolds numbers between 258 and 920. The average Nusselt number was calculated for each experiment and plotted as function of the Reynolds and Dean numbers. Three distinct regions of the average Nusselt number were observed in the curved section when compared with the straight section. The presence of Taylor-Goertler vortices in the curved section was verified from the distribution of the liquid crystal color bands. It was concluded that the overall effect of the vortices whenever they occurred was to improve the heat transfer process from the curved section. (Author)

Une note sur la propriété de préfixe

Abstract: We give a necessary and sufficient condition for a language with the prefix property of R.V. Book to be regular.

A generalization of leftmost derivations

Abstract: A generalization of leftmost derivation called depth-first derivation is defined. The main result, that the depth-first derivations of an arbitrary phrase-structure grammar generate a context-free language, is proved using a new technique in which families of equivalent depth-first derivations of one grammar are represented by single productions in a new grammar. This result is related to several others, including an analogous result for leftmost derivations, through the theorem of B. Baker [1] that every terminal-bounded grammar generates a context-free language.

Maneuvering target simulation for testing the terminal guidance of air-to-air missiles

Abstract: : There was a need for a complete maneuvering target for air-to-air combat simulation. A computer program was developed with logic and tactical decisions subroutines. The parameters for these decisions corresponded to the differences in pilots and the relative aircraft states. The decision subroutines provided the desired control inputs to accomplish the required maneuvers. Validation of the simulated target was accomplished by use of five test runs from different initial conditions as well as twenty runs from the same initial conditions. (Author)

AMPLITUDE SCINTILLATIONS ON EARTH-SPACE PROPAGATION PATHS AT 2 AND 30 GHz

Abstract: Amplitude scintillation measurements were made simultaneously at 2.075 and 30 GHz on earth-space propagation paths over elevation angles in the range 0.4 to 44 deg. The experiment was performed as the Applications Technology Satellite (ATS-6) was moved slowly from a synchronous position over Africa to a new synchronous position over the United States. The received signal, variance, level, covariance, spectra and fade distributions are discussed as functions of the path elevation angle. These results are also compared wherever possible with similar measurements made earlier at 20 and 30 GHz.

On the characterization of linear and linearizable automata by a superposition principle

Abstract: This paper deals with the superponability of linear and linearizable automata. Automata linear in GF(p),p2, with input and output sets {0, 1,⋯,p-1} and with arbitrary initial state are characterized as the class of automata superponable, i.e. permutable, with respect to a functionax+(1-a)x′. The casep=2 requires special considerations. The inputoutput behaviour of this automata can be described by generalized impulse responses. Using instead of GF(p) an arbitrary commutative field on the same basic set {0,1,⋯,p-1} some of the functions nonlinear in GF(p) are linear in this field. These functions are called linearizable. Linearizable functions are characterized by a functional equation and solvability conditions and as polynomials in GF(p). Thus the well known theory of linear automata can be extended to linearizable automata.

Phase-lock control considerations for multiple, coherently combined lasers

Abstract: : This paper presents design considerations and fundamental performance limitations of phase-lock control loops used to coherently combine an array of lasers. A two-laser control loop designed to lock the differential frequency/phase between two lasers to a specified reference is first investigated. An integro-differential equation, valid for the linearized operating region of the loop, is derived in terms of the specified (desired) phase control, the phase measurement (heterodyne) noise, and the laser phase noise (instabilities). Solution of the equation results in an expression for the lasers' phase error variance in terms of the closed-loop noise equivalent bandwidth, the 100 measurement noise, and the lasers' field linewidths. Loop acquisition time, frequency pull-in range, and steady state phase error are also examined.

Interfacial flow patterns on a static liquid drop with forced internal circulation

Abstract: In the absence of interfacial turbulence and mass transfer, the interfacial motion on a forming liquid drop results purely from shear transmitted by internal motion of the fluid inside the drop, just underneath the interface. The shear-induced motion in the interface was observed by placing light reflecting hollow glass beads on the interface of a static liquid drop with forced internal circulation and photographing their motion. Two, four, and six symmetrical flow patterns were observed on the interface when the Reynolds number based on the density and viscosity of the drop fluid, the velocity through nozzle, and the nozzle diameter was varied over a range of 8 to 34, 60 to 150, and 220 to 270, respectively. The shape of each of the two pattern flows was approximately elliptical, while that of the four and six pattern flow was approximately triangular. The gradual change from two to four, and four to six patterns occurred in the range of Reynolds number 34 to 60, and 150 to 220, respectively. No distinguishable motion was observed at Reynolds numbers less than 8.

Corrigendum: Context free languages and rudimentary attributes

Abstract: Proof--Only If. We show P(rcc's) implies P(rs). To see that this suffices, let P(x) hold for x # A , and write x = ucv where v E(C')*. By definition of P we can write v = c'v', so x---ucc'v'. Thus P(uv') holds. Repeating, we can progressively cancel x to A, so x ~ D. Now, suppose P(rcc's) holds, and rs= uciv. If this c/lies within s, P(rcc's) implies H(civ ) ends in c i. Otherwise we may write rs=uciws for some w (so v= ws). Consider H(ciwcc's): by P(rcc's) this is nonempty and ends in c;. If H(ciwcc's)=H(ciw), clearly H(civ)=H(ciw ) and so H(civ ) ends in ci' as required. The only remaining possibility is H(ciwcc's)=ciwcc't for some t~A. In this case ciwt is balanced and ends in c,.', so qwt is a balanced nonempty prefix of civ. It must also be shortest since otherwise c~wcc't~ H(ciwcc's). Thus H(civ ) ends in c; as required. If. We show P (rs) implies P (rcc's). This suffices, since if x ~ D there must be a sequence X=Xl,X 2 . . . . , x , = A where xi+ ! is obtained from x i by deleting a substring cc'. P(A) is trivially true and P(xi+l) implies P(xi) , so P(x) also holds.

Continuous operations on languages

Abstract: Most of the operations of interest in language theory arecontinuous in a certain technical sense. For such operations, there always exist infinite sets of languages that areindependent in the sense that no language in such a set can be generated from the other languages in the set by the operations in question.

A theoretical analysis of changes in thermal signatures caused by physical and climatological factors

Abstract: : An investigation of the thermal signatures of natural objects is undertaken. Using the principle of energy balance, diurnal temperature models are developed for the ground, a vehicle (such as a tank), and the leaves of a tree. These models are included in a computer program designed to simulate daily variations in conductive, radiative, and convective heat transfer processes. Environmental conditions are changed by altering the program inputs, which include; latitude, day, wind speed, mean air temperature, cloud type, total insolation, absolute and relative humidity, atmospheric pressure, and particular concentration. The program is iterated for several values of a single parameter such as one of the environmental inputs, or one of 21 physical characteristics of the models (for example; ground reflectivity, tank thickness, or leaf transpiration rate). There are two types of output from the program; simultaneous plots of the temperatures of all the models for a 30-hour period, and curves representing 24-hour periods of the temperature difference (Delta-T) between the tank and the ground. The effects of changing a parameter are analyzed by comparing the various Delta-T curves.

The utilization of broadband antennas in military tactical communications nets

Abstract: : This thesis investigates the characteristics of current and developmental broadband antennas used with low and medium power, frequency modulated radio equipment operating in the 30-76 MHz frequency range in military tactical voice radio communication nets. The radio communication net structure of the Airborne and Airmobile Infantry combat units of the Airborne and Air Assault Divisions are used to display data on density of equipment, typical communications ranges, and problems encountered by tactical communications-electronics personnel in providing reliable, secure, responsive, and flexible radio communications within the battle area. Data for the study were assembled from current military communications-electronics and electronic warfare training literature, military communications engineering references, standard electrical engineering textbooks on antenna analysis and design, research and development technical reports submitted to and by the communications-electronics research and development agencies of the United States Army and Marine Corps, and equipment specification sheets and test reports obtained from various manufacturers of military communications-electronics equipment. The results of this study, combined with field testing of various items of radio and antenna equipment conducted at military installations throughout the United States and West Germany, show that use of wideband omnidirectional and, particularly, wideband directional antennas can enhance both the communications reliability and flexibility of combat units, and at the same time provide a much greater degree of communications security and defense against enemy electronic countermeasures.