Synthesis of multifunction and universal logic elements over residue class rings. I

Translated from Kibernetika, No. 4, pp. 89–94, July–August, 1988.     

Singular shift registers over residue class rings

The study of shift registers over the ringZ _p ^r (p a prime,r 1), in particular the singular case, is carried out, giving necessary and sufficient conditions to make a shift register singular. Its state graph is characterized as a tree, whose form depends on the characteristic polynomial of the shift register. The relationships with singular shift register overZ _p are explored and a proof of their equivalence is presented.Research sponsored by the National Science Foundation, Grant GK-1065x, and the Joint Services Electronics Program, Grant AFOSR-68-1488.Part of this work was done while the author was at Electronics Research Laboratory, University of California at Berkeley.     

Distribution of r-tuples in one class of uniformly distributed sequences over residue rings

We consider the distribution of r-tuples in one class of uniformly distributed linear recurring sequences over residue rings. We establish bounds for the number of occurrences of a given r-tuple and prove that these bounds are asymptotically the best possible.     

Equidistributed sequences over finite fields produced by one class of linear recurring sequences over residue rings

We consider the distribution of r-patterns in one class of uniformly distributed sequences over a finite field. We establish bounds for the number of occurrences of a given r-pattern and prove upper bounds for the cross-correlation function of these sequences.     

Tunable multifunction logic modules based on parametric representation of functions of k-valued logic over quasifields

We propose a new class of tunable logic modules that realize functions of k-valued logic. These modules are characterized by homogeneous structure and linear dependence of the number of tunable inputs on the number of input variables.Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 24–29, July–August, 1991.     

A universal logic element over the complex field

We propose a mathematical model of the universal logic element using a parametric representation of Boolean functions over the complex field.Translated from Kibernetika, No. 3, pp. 116–121, May–June, 1991.     

A class of 1-generator quasi-cyclic codes over finite chain rings

Using another method, which is different with the one given by Cao [1-generator quasi-cyclic (QC) codes over finite chain rings, Appl. Algebra Eng. Commun. Comput. 24 (2013), pp. 53–72], we investigate the structural properties of a class of 1-generator QC codes over finite chain rings. We give the structure of the annihilator of 1-generator QC codes, the conditions for 1-generator QC codes to be free and the minimum distance bounds on 1-generator QC codes. Under some conditions, we also discuss the enumeration of 1-generator QC codes and describe how to obtain the one and only one generator for each 1-generator QC code.     

Synthesis of feedback control logic for a class of controlled Petrinets

An efficient solution is developed for a class of forbidden state problems for discrete event systems (DESs). DESs are considered which can be modeled as cyclic controlled marked graphs (CMGs), a special class of controlled Petri nets (CPNs). The distributed representation of the DES state in terms of the CMG marking permits an efficient specification of the forbidden states in terms of individual place markings. More important, it is shown that the graphical representations of the state transition logic in a CMG can be used to synthesize state feedback logic which is maximally permissive while guaranteeing the forbidden states will not occur. The practical application of the theoretical results is illustrated for an example of automated guided vehicle (AGV) coordination in a flexible manufacturing facility     

A comparison of voice and multifunction controls: logic design is the key

The proper design of the human-computer interface is a key feature for the optimum use of advanced manned systems. In future aircraft cockpits, one of the pilot's principle tasks will be to interact with a very sophisticated computer system—an electronic crewmember. This paper discusses the experimental comparison of two communication mechanisms: voice control and multifunction keyboards. The paper also discusses the crucial role of the software logic used with these devices.     

泛逻辑学中UB代数系统的若干性质

文[1]提出了理想状态（h=k=0.5）下泛逻辑学对应的代数系统-UB代数,给出了它的一些性质。在[1]的基础上,进一步讨论了UB代数系统,得到一些有趣的结果,这些结果对UB代数的进一步研究是有用的。     

基于零级泛与运算的泛逻辑中广义重言式理论

对泛逻辑的广义重言式理论进行了研究,给出了基于零级泛与运算的广义重言式的一系列性质。主要结果有:当c∈[0.75,1]时,关于Ih=c而言,F(S)中只有3种不同的广义重言式,即可达0-重言式、0+-重言式和重言式;当h=0时,关于Ih=0而言,F(S)中存在0、1可达重言式,当α∈(0,1),不存在α-重言式、α+-重言式和可达α-重言式;用h=0.5时的广义重言式对h∈(0,0.75)时的广义重言式进行了刻画。     

泛逻辑学中UB代数系统的滤子与商代数

给出了理想状态下泛逻辑学的形式演绎系统,证明了此系统是可靠的。提出了在理想状态（h=k=0.5）下泛逻辑学对应的代数系统-UB代数,进一步讨论了UB代数滤子与商代数,得到一些有用的结果。     

泛逻辑学中UB代数系统的fuzzy滤子

文献[2]给出了理想状态下泛逻辑学的形式演绎系统!,证明了此系统是可靠的。文献[3]提出了在理想状态(h=k=0.5)下泛逻辑学对应的代数系统-UB代数。文献[5]研究了泛逻辑学中UB代数系统的若干性质。在文献[3,5]的基础上,进一步讨论了UB代数fuzzy滤子与商代数。     

Clausal intuitionistic logic II. tableau proof procedures

Clausal intuitionistic logic is an extension of Horn-clause logic which permits the appearance of negations and embedded implications on the right-hand side of a rule, and interprets these new rules intuitionistically in a set of partial models. In this article the second of a pair, clausal intuitionistic logic, is shown to have a tableau proof procedure that generalizes Horn-clause refutation proofs. The proof procedures are explained by means of several detailed examples. Soundness and completeness theorems are stated and proven in full detail.     

Efficient logic design of reliable control units. II

Two autogram-based formal methods of construction of control units from nontransparent flip-flops are described. One of them is a simplification of a frequently used (classical) method for design of control units. The results of synthesis under this method are easily interpreted in terms of the initial statement of a design problem. The other method is a generalization of the classical method. It allows one to optimize areas and realize control units using standard unified blocks. Both methods can be easily used within the framework of CAD tools.     

Design of a universal logic block for fault-tolerant realization of any logic operation in trapped-ion quantum circuits

This paper presents a physical mapping tool for quantum circuits, which generates the optimal universal logic block (ULB) that can, on average, perform any logical fault-tolerant (FT) quantum operations with the minimum latency. The operation scheduling, placement, and qubit routing problems tackled by the quantum physical mapper are highly dependent on one another. More precisely, the scheduling solution affects the quality of the achievable placement solution due to resource pressures that may be created as a result of operation scheduling, whereas the operation placement and qubit routing solutions influence the scheduling solution due to resulting distances between predecessor and current operations, which in turn determines routing latencies. The proposed flow for the quantum physical mapper captures these dependencies by applying (1) a loose scheduling step, which transforms an initial quantum data flow graph into one that explicitly captures the no-cloning theorem of the quantum computing and then performs instruction scheduling based on a modified force-directed scheduling approach to minimize the resource contention and quantum circuit latency, (2) a placement step, which uses timing-driven instruction placement to minimize the approximate routing latencies while making iterative calls to the aforesaid force-directed scheduler to correct scheduling levels of quantum operations as needed, and (3) a routing step that finds dynamic values of routing latencies for the qubits. In addition to the quantum physical mapper, an approach is presented to determine the single best ULB size for a target quantum circuit by examining the latency of different FT quantum operations mapped onto different ULB sizes and using information about the occurrence frequency of operations on critical paths of the target quantum algorithm to weigh these latencies. Experimental results show an average latency reduction of about 40 % compared to previous work.     

The simulation of texture evolution with finite elements over orientation space II. Application to planar crystals

In a companion paper, a new class of finite element schemes was presented for the modeling of arbitrary polycrystalline microstructure. In this work, these schemes are applied to the idealization of a planar microstructure. Reorientation velocities, obtained under particular macro-micro linking hypothesis and crystal constitutive relations, are examined over a range of rate sensitivities, and for a range of planar crystal geometries. It is shown that, under monotonic deformations, equilibria of the reorientation velocity determine the asymptotic structure of the developed reorientation entirely. A one-parameter characterization of reorientations by their asymptotic structures is developed, and exploited to display the entire range of reorientation structures in a set of bifurcation diagrams. Texturing representative of the range of qualitatively distinct reorientation structures is simulated using an updated Lagrangian finite element scheme.     

Algorithms for solving systems of linear diophantine equations in residue rings

Algorithms are proposed that construct the basis of the set of solutions to a system of homogeneous or inhomogeneous linear Diophantine equations in a residue ring modulo n when the prime factors of n are known. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 27–40, November–December 2007.