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The sequentially realizable functionals

John Longley
<span title="">2002</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bnojym2hjzcgnpa4wixi2axhnq" style="color: black;">Annals of Pure and Applied Logic</a> </i> &nbsp;
We consider a notion of sequential functional of finite type, more generous than the familiar notion embodied in Plotkin's language PCF.  ...  We also consider the relationship between our notion of sequentially computable functional and other known notions of higher-type computability.  ...  In this paper the higher-type functionals in question will be called the sequentially realizable (or SR) functionals, as distinguished from the PCF-sequential functionals.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0168-0072(01)00110-5">doi:10.1016/s0168-0072(01)00110-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hgfzu3drjfdnpdunhpeb2wyncq">fatcat:hgfzu3drjfdnpdunhpeb2wyncq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809050231/http://homepages.inf.ed.ac.uk/jrl/Research///srf.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/30/3f/303f0b9f1b07d9cbde9c27648a23be39934e33b5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0168-0072(01)00110-5"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

The Sequentially Realizable Functionals [chapter]

John Longley, Dag Normann
<span title="">2015</span> <i title="Springer Berlin Heidelberg"> Higher-Order Computability </i> &nbsp;
We consider a notion of sequential functional of finite type, more generous than the familiar notion embodied in Plotkin's language PCF.  ...  We also consider the relationship between our notion of sequentially computable functional and other known notions of higher-type computability.  ...  In this paper the higher-type functionals in question will be called the sequentially realizable (or SR) functionals, as distinguished from the PCF-sequential functionals.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-662-47992-6_11">doi:10.1007/978-3-662-47992-6_11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dp2n5wmdgze27ioi3fmwc63psm">fatcat:dp2n5wmdgze27ioi3fmwc63psm</a> </span>
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Serial realization of the next state and output functions of a sequential machine

Giuseppe Gestri
<span title="">1972</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fbkexx2qg5anljkxraobuswdq4" style="color: black;">Information and Control</a> </i> &nbsp;
It is shown that the serial realization of the next state and output functions of a sequential machine, if possible, m a y be m o r e convenient than the parallel one.  ...  The assignments that reduce the functional dependence for the serial realization can be obtained by appropriate partition pairs.  ...  INTRODUCTION To realize a sequential machine M two functions must be realized, the next state function 3 and the output function A.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0019-9958(72)90141-6">doi:10.1016/s0019-9958(72)90141-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/esni5745qjcpxlq6oza5ff47ma">fatcat:esni5745qjcpxlq6oza5ff47ma</a> </span>
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Page 2190 of Mathematical Reviews Vol. 50, Issue 6 [page]

<span title="">1975</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The author studies sequential functions or input-output relations of fuzzy systems which are realizable by maximin machines.  ...  Usually the definitions of the next-state-function 8 and the output function A of a Mealy-type sequential machine S(¢+1)= 8(S(t), 1(t)); O(t)=A(S(t+1), [(t)) suggest a parallel realization of the subnetworks  ... 
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One Step at a Time: The Origins of Sequential Simulation and Beyond

J. Jaime Gómez-Hernández, R. Mohan Srivastava
<span title="2021-02-05">2021</span> <i title="Springer Science and Business Media LLC"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5v5daj5lgfgv3p5hr7m65qpojy" style="color: black;">Mathematical Geosciences</a> </i> &nbsp;
The early enthusiasm for SIS was its ability, in its multiple-indicator form, to cure the Gaussian disease and to build realizations in which spatial continuity did not deteriorate in the extreme values  ...  early indicator simulations went through the tortuous path of converting all indicators to Gaussian variables, running a turning bands simulation, and truncating the resulting multi-Gaussian realizations  ...  Acknowledgements The first author wishes to acknowledge the financial contribution of the Spanish  ... 
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Page 7837 of Mathematical Reviews Vol. , Issue 2003j [page]

<span title="">2003</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The sequentially realiz- able functionals are the elements of (the interpretations of) the simple types in this category.  ...  This paper investigates the type structure of the sequentially realiz- able (SR) functionals. Such functionals provide a possible charac- terization of higher-type sequential computation.  ... 
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Page 894 of Automation and Remote Control Vol. 25, Issue 6 [page]

<span title="">1964</span> <i title="Springer Science &amp; Business Media"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_automation-and-remote-control" style="color: black;">Automation and Remote Control </a> </i> &nbsp;
SIMPLEST SEQUENTIAL ELEMENTS (FLIP-FLOPS) AND THEIR APPLICATION AS MEMORY ELEMENTS IN THE REALIZATION OF SEQUENTIAL FUNCTIONS (UDC 62-507.15) N. P. Vasil'eva and J. A.  ...  of the sequential function.  ... 
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Radix enumeration of rational languages

Pierre-Yves Angrand, Jacques Sakarovitch
<span title="">2010</span> <i title="EDP Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/foywj2stzfcwdln5izx2cxkroe" style="color: black;">RAIRO - Theoretical Informatics and Applications</a> </i> &nbsp;
We prove that the function that maps a word of a rational language onto its successor for the radix order in this language is a finite union of co-sequential functions.  ...  A rational function is sequential (resp. co-sequential) if it is realized by a sequential (resp. co-sequential) transducer. Remark 1.  ...  For every i and j, A i ⋊ ⋉ < < < B j is a sequential transducer and realizes the same function as A i ⋊ ⋉ B j .  ... 
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Shift register realizations of asynchronous sequential machines

Yueh-Hsung Su
<span title="">1969</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fbkexx2qg5anljkxraobuswdq4" style="color: black;">Information and Control</a> </i> &nbsp;
The realization of this paper can be used to realize definite events which are free of critical races. REALIZATIONS OF ASYNCHRONOUS SEQUENTIAL MACHINES 233  ...  Therefore, the realization brings closer together the theories of synchronous and asynchronous sequential machines.  ...  FUNCTION ARRAY REPRESENTATION OF DEFINITE ASYNCHRONOUS SEQUENTIAL MACHINES Any finite memory synchronous sequential machine can be expressed by a function array [15, 16, 18] (function table) ; the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0019-9958(69)90435-5">doi:10.1016/s0019-9958(69)90435-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3xmkgs5etvemlf25tempxhlvl4">fatcat:3xmkgs5etvemlf25tempxhlvl4</a> </span>
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Page 1110 of Mathematical Reviews Vol. 56, Issue 3 [page]

<span title="">1978</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
In order to explore the limitations imposed by the requiremens of the realization of a sequential system by an Ism, definitions for various types of realizations of one sequential system by another are  ...  It follows from the above that in order to find the limits to whicha sequential system can be realized by an Ism it is necessary to consider the most general case of linear realization.  ... 
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Every finite sequential machine is linearly realizable

G.T. Herman
<span title="">1971</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p6ovb2qpkfenhmb7mcksobrcxq" style="color: black;">Journal of computer and system sciences (Print)</a> </i> &nbsp;
We prove that, using the definitions of realization of one sequential machine by another which appear to be most widely accepted today, every finite sequential machine is linearly realizable over any field  ...  We shall show that our result is the strongest we can hope for, putting various additional restrictions on the definition of linear realizability would result in the existence of not linearly realizable  ...  We shall say that a sequential machine M --(Q, Z, A, 3, ~> isfinite when Q, Z, and A are finite. It is necessary to extend the transition function and the output function.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0022-0000(71)80012-0">doi:10.1016/s0022-0000(71)80012-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5xczoxaw3bgx3aj7r7f66xziq4">fatcat:5xczoxaw3bgx3aj7r7f66xziq4</a> </span>
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Every discrete input machine is linearly simulatable

Bernard P. Zeigler
<span title="">1973</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p6ovb2qpkfenhmb7mcksobrcxq" style="color: black;">Journal of computer and system sciences (Print)</a> </i> &nbsp;
Since this permits the computation of nonrecursive functions, it is concluded that allowing nonlinear output decoding with infinite state linear machines leads to a triviality (as opposed to the case of  ...  This paper extends the work of Herman (1971) to show that all discrete input sequential machines (whether finite or infinite state) are linearly simulatable over fields of infinite characteristic.  ...  The (nonlinear) output decoder 7a: c(I+) --+ Z is given by %(c(x)) = f(x) c(x), 71(a))) ~-72(mc(x) -~ a) Given a finite input sequential function f, any connected machine which realizes f is linearly homomorphically  ... 
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Page 1535 of Automation and Remote Control Vol. 26, Issue 9 [page]

<span title="">1965</span> <i title="Springer Science &amp; Business Media"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_automation-and-remote-control" style="color: black;">Automation and Remote Control </a> </i> &nbsp;
The present paper deals with another problem, namely, the problem of the exact (down to an accounting of unstable states) realization of any given sequential function by various sets of actual (i,e., real  ...  CONDITIONS FOR EXACT REALIZATION OF SEQUENTIAL FUNCTIONS BY VARIOUS SETS OF ACTUAL LOGICAL ELEMENTS, ACCOUNT BEING TAKEN OF LAGS (UDC 681,142.67) N. P. Vasil'eva and I.  ... 
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A Study on Construction of the Advanced Sequential Circuit over Finite Fields

Chun-Myoung Park
<span title="2019-12-31">2019</span> <i title="Korea Multimedia Society - English Version Journal"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3opa2pn4xbcpbm4lhsp62jqtuu" style="color: black;">Journal of multimedia information system</a> </i> &nbsp;
The following status functions were derived from the status function and the preceding table, and the T-gate and the device were used to construct the sequential circuit.  ...  For this purpose, the state transition diagram was allocated to the state dependency code and a whole table was drawn showing the relationship between the status function and the current state and the  ...  we obtain the state function are as following Equations Fig. 4 . 4 The circuit realization of the sequential digital systems forFig. 3.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.33851/jmis.2019.6.4.323">doi:10.33851/jmis.2019.6.4.323</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fioahjvenzd5rahiwvudubie4q">fatcat:fioahjvenzd5rahiwvudubie4q</a> </span>
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Synthesis of Sequential Reversible Circuits through Finite State Machine [article]

Shubham Gupta
<span title="2015-01-07">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
However the realization of sequential circuit in reversible logic is still at premature stage. Sequential circuits were not available because of feedback was not allowed in reversible circuit.  ...  We expect that the sequential reversible circuits will help in debugging the reversible circuits, handling the ambiguous state of an FSM and generating the original input in reverse direction by reversing  ...  In other words, the input C must be constant zero to realize the function. A, B are two garbage outputs. This function realizes the Toffoli gate [6] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1410.2370v3">arXiv:1410.2370v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cnxml765tjhahoaesdtphrgrcq">fatcat:cnxml765tjhahoaesdtphrgrcq</a> </span>
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