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Page 938 of Mathematical Reviews Vol. 14, Issue 10 [page]

1953 Mathematical Reviews  
Concatenation as basis for a complete system of arithmetic. J. Symbolic Logic 18, 1-6 (1953).  ...  Using a limited kind of universal quantification in place of the proper ancestral and concatenation in place of the ordered-pair function as primitive operators, complete sys- tems for arithmetic are constructed  ... 

A CHARACTERIZATION OF THE ARITHMETICAL HIERARCHY BY LANGUAGE EQUATIONS

ALEXANDER OKHOTIN
2005 International Journal of Foundations of Computer Science  
Language equations with all Boolean operations and concatenation and a particular order on the set of solutions are proved to be equal in expressive power to the first-order Peano arithmetic.  ...  In particular, it is shown that the class of sets representable using k variables (for every k 2) is exactly the k-th level of the arithmetical hierarchy, i.e., the sets definable by recursive predicates  ...  Here it is used as the basis of induction for the representation of the upper levels of the arithmetical hierarchy. Let us explain its essential idea.  ... 
doi:10.1142/s012905410500342x fatcat:cmm3larvaza6vjfjq2c6abxgre

JSL volume 18 issue 1 Cover and Front matter

1953 Journal of Symbolic Logic (JSL)  
TABLE OF CONTENTS OF Concatenation as basis for a complete system of arithmetic. By M. H. LOB 1 Criteria of constructibility for real numbers. By JOHN MYHILI 7 On truth and multiple denotation. By R.  ...  By LEON HENKIN . 1 9 On axiomatizability within a system. By WILLIAM CRAIG . . . . . . 30 Arithmetical problems and recursively enumerable predicates.  ... 
doi:10.1017/s0022481200098091 fatcat:sftrqey5mvd6veaqn3hfkxzawi

Automatic abstraction and verification of verilog models

Zaher S. Andraus, Karem A. Sakallah
2004 Proceedings of the 41st annual conference on Design automation - DAC '04  
Vapor performs a sound abstraction with emphasis on minimizing false errors. Our method is fast, systematic, and complements UCLID by serving as a back-end for dealing with UCLID counterexamples.  ...  A number of languages have been proposed to model hardware systems by, primarily, abstracting away their wide datapaths while keeping the low-level details of their control logic.  ...  The authors would like to thank Randy Bryant and his group in Carnegie Mellon, for their assistance in using and understanding UCLID.  ... 
doi:10.1145/996566.996629 dblp:conf/dac/AndrausS04 fatcat:uytmmfd4tbbxtcwpw3sfchs3ia

Computer algebra on MIMD machine

J.-L. Roch, P. Senechaud, F. Sievert-Rich, G. Villard
1989 ACM SIGSAM Bulletin  
PAC is a computer algebra system, based on MIMD type parallelism. It uses parallelism as a tool for processing problems wich are too complex for a sequential treatment.  ...  Then, different problems are studied, particularly the implementation of infinite-precision arithmetic, the solution of linear systems and of Diophantine equations, the parallelization of Buchberger's  ...  However, it is possible to use other basis. Conversions in 109 basis are made by the user interface. Rationals are stored in array -as the concatenation -of two integers.  ... 
doi:10.1145/66062.66065 fatcat:y2pcdfwedrb2hdzjifvf5ncrue

A transfer principle for second-order arithmetic, and applications [article]

Merlin Carl, Asgar Jamneshan
2019 arXiv   pre-print
In this paper, we formulate and prove such a transfer principle based on second-order arithmetic, which, by the results of reverse mathematics, suffices for the bulk of classical mathematics, including  ...  In the theory of conditional sets, many classical theorems from areas such as functional analysis, probability theory or measure theory are lifted to a conditional framework, often to be applied in areas  ...  Metric spaces In the axiomatic system of second-order arithmetic, the only definable metric spaces are separable and complete ones which are coded as a completion of a countable set with a prescribed rate  ... 
arXiv:1804.01573v5 fatcat:yhzavcfefbguhack3i4inoy4mq

Implementation of Fast and Efficient Mac Unit on FPGA

Sachin Raghav, Rinkesh Mittal
2016 International Journal of Mathematical Sciences and Computing  
Floating-point arithmetic operations on digital systems have become an important aspect of research in recent times.  ...  FP operation is utilized for some real time applications in multimedia and graphics and also in DSP processor. as it gives extensive range of real numbers.  ...  It has the capability to enhance the arithmetic precision of algorithm as rounding steps have reduced.  ... 
doi:10.5815/ijmsc.2016.04.03 fatcat:qpsjx2t43fd3xgvxzavttffpda

JSL volume 18 issue 4 Cover and Front matter and Errata

1953 Journal of Symbolic Logic (JSL)  
New subscriptions must begin with the first number of the current volume, as determined by the date of receipt of the subscription. Completed volumes are sold at six dollars.  ...  Members of-the Association of three years standing may purchase back volumes of the JOURNAL at'reduced rates for their personal use (except volume 1). 6, Wisconsin or to Alice A.  ...  TABLE OF CONTENTS OF Concatenation as basis for a complete system of arithmetic. By M. H. L O B 1 Criteria of constructibility for real numbers.  ... 
doi:10.1017/s0022481200088757 fatcat:fdf4snqq2rd7tkqjmtd4begcxi

Initial Algebra for a System of Right-Linear Functors

Anna Labella, Rocco De Nicola
2017 Acta Cybernetica  
In this note, we prove that a right-linear system of polynomial endofunctors on a cocartesian monoidal closed category which enjoys parameterized left list arithmeticity, has an initial algebra, provided  ...  In 2003 we showed that right-linear systems of equations over regular expressions, when interpreted in a category of trees, have a solution whenever they enjoy a specific property that we called hierarchicity  ...  Structured sets of computations are organised as a category of generalised trees built over a (complete) meet-semilattice monoid generated from A.  ... 
doi:10.14232/actacyb.23.1.2017.12 fatcat:njzuwmjhczgfxcphtipdw43m7m

Page 1756 of Mathematical Reviews Vol. 51, Issue 6 [page]

1976 Mathematical Reviews  
The authors demonstrate that, for any arithmetically minimal system R, if ae Field(R) and |a|zp=w-a+i, i<w, then H¥(a) is constructed at level a+ 1 of the Gédel hierarchy, thus completing the circle.  ...  In the present paper, the authors consider arithmetically minimal systems, i.e., systems R such that, for any system S, ((a € Field(R) & b € Field(S) & |a\p=|b|;)— H*(a) is arithmetical in H%(b)).  ... 

Integrated logic circuits using single-atom transistors

J. A. Mol, J. Verduijn, R. D. Levine, F. Remacle, S. Rogge
2011 Proceedings of the National Academy of Sciences of the United States of America  
The analysis of the operation of an experimental realization of a full adder in the gas phase using electronic spectroscopy (33) is also based on the physics of a multilevel system.  ...  The fundamental and crucial advance is that here we report on the response of a single atom and not of an ensemble as is the case for addressing in the gas phase or in solution.  ...  This stepwise behavior of the current is the physical basis for the multivalued processing of the addition of the two binary numbers A and B.  ... 
doi:10.1073/pnas.1109935108 pmid:21808050 pmcid:PMC3161576 fatcat:kapxqwy4sfdgfd2tdjgshzimoq

A transfer principle for second-order arithmetic, and applications

Merlin Carl, Asgar Jamneshan
2018 Journal of Logic and Analysis  
More precisely, we prove that any consequence of the second-order axiomatic system of arithmetical comprehension ACA 0 , which has a second-order comprehension axiom for formulas in which all quantifiers  ...  As new consequences, we obtain conditional versions of the Peano existence theorem, Urysohn's lemma, the existence of an orthonormal basis and the Markov-Kakutani theorem.  ...  Metric spaces In the axiomatic system of second-order arithmetic, the only definable metric spaces are separable and complete ones which are coded as a completion of a countable set with a prescribed rate  ... 
doi:10.4115/jla.2018.10.8 fatcat:hxdalrg4pbeq7drq27rcmzfnci

On Equations over Sets of Integers

Artur Jez, Alexander Okhotin, Marc Herbstritt
2010 Symposium on Theoretical Aspects of Computer Science  
Testing whether a given system has a solution is Σ 1 1 -complete for each model.  ...  Systems of equations with sets of integers as unknowns are considered.  ...  Note, that the basis of the induction are ≺-minimal elements n of A, as for them φ(n) has to be shown directly. Fix B i 0 as the target set in the root.  ... 
doi:10.4230/lipics.stacs.2010.2478 dblp:conf/stacs/JezO10 fatcat:3ogfa35oczg6hiolb7ijufcb7e

Discordant Compact Logic-Arithmetic Structures in Discrete Optimization Problems [article]

V. F. Romanov
2013 arXiv   pre-print
As a result the problem of the formula satisfiability is reduced to the following one: ascertain the fact of existence (or absence) of a "joint satisfying set" (JSS) for all discordant structures, based  ...  and arithmetic interpretation of data.  ...  For completeness of a picture as a whole we consider the procedure action for the alternative value of the starting variable: a = 1 (¬a = 0).  ... 
arXiv:1309.6078v1 fatcat:s5fu545scfa4dismnsepxcurhi

The ModelCC Model-Driven Parser Generator

Fernando Berzal, Francisco J. Cortijo, Juan-Carlos Cubero, Luis Quesada
2015 Electronic Proceedings in Theoretical Computer Science  
This grammar is then annotated with semantic actions for the resulting system to perform its desired function.  ...  ModelCC receives a conceptual model as input, along with constraints that annotate it.  ...  Acknowledgements Work partially supported by research project TIN2012-36951, "NOESIS: Network-Oriented Exploration, Simulation, and Induction System", funded by the Spanish Ministry of Economy and the  ... 
doi:10.4204/eptcs.173.5 fatcat:sbugo52nzbfgjmp3wjy32ylklm
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