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Biconditional BDD: A Novel Canonical BDD for Logic Synthesis Targeting XOR-rich Circuits

2013
*
Design, Automation & Test in Europe Conference & Exhibition (DATE), 2013
*

To exploit this opportunity

doi:10.7873/date.2013.211
dblp:conf/date/AmaruGM13
fatcat:y2dcpzufsjgw5ayanvhn3cvefq
*in**logic*synthesis for XOR-rich circuits, we developed a BBDD-based One-Pass Synthesis (OPS) methodology. ... Since the biconditional expansion is based on the XOR/XNOR operations, XOR-rich*logic*circuits are efficiently represented and manipulated with canonical Reduced and*Ordered*BBDDs (ROBBDDs). ...*In*this context, the quality of the synthesized circuit depends on the ROBBDD*compactness*.*Ordering*and reduction rules make the ROBBDD construction efficient and unique. ...##
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Page 23 of Mathematical Reviews Vol. , Issue 98A
[page]

1998
*
Mathematical Reviews
*

*In*

*order*for Q to qualify as a

*logical*quantifier, q is required to be closed under isomorphisms. ... Sci. 166 (1996), no.

*1*-2, 63-81. Summary: “By augmenting first-

*order*

*logic*with monadic parti- tion quantifiers we obtain a new family of extended

*logics*. ...

##
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Lindstrom theorems for fragments of first-order logic

2007
*
22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)
*

Examples of abstract

doi:10.1109/lics.2007.29
dblp:conf/lics/CateBV07
fatcat:brerbh77lva7jecj4pqlj2m3de
*logics**in*this sense include first-*order**logic*(F O) and its k-*variable*fragments (F O k ), with k ≥*1*. ... VÄÄNÄNEN Figure*1*: Fragments of first-*order**logic*The first-*order*Lindström Theorem [13] An extension of first-*order**logic*satisfies*Compactness*and the Löwenheim-Skolem property if and only if it is no ... include basic modal*logic*, its extension with counting modalities called graded modal*logic*(GM L), first-*order**logic*(by which we mean the collection of all first-*order*formulas*in*one free*variable*, ...##
###
PC-compactness, a necessary condition for the existence of sound and complete logics of partial correctness
[chapter]

1984
*
Lecture Notes in Computer Science
*

A first

doi:10.1007/3-540-12896-4_354
fatcat:4d66r3rjwrb4fpmjqak2uuujoa
*order*theory is called PC-*compact*if each asserted program which is true*in*all models of the theory is true*in*all models of a finite subset of the theory. ... If a structure has a complete Hoare's*logic*then its first*order*theory must be PC-*compact*; moreover, its partial correctness theory must be decidable relative to this first*order*theory. ... Let x*1*, x 2 be*variables*for N and y*1*, y 2 be*variables*for AO. ...##
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Lindström theorems for fragments of first-order logic

2009
*
Logical Methods in Computer Science
*

Lindstr\"om theorems characterize

doi:10.2168/lmcs-5(3:3)2009
fatcat:efpyabo6rrfhnexfqesab5fkby
*logics**in*terms of model-theoretic conditions such as*Compactness*and the L\"owenheim-Skolem property. ...*In*this paper, we provide Lindstr\"om theorems for several fragments of first-*order**logic*, including the k-*variable*fragments for k>2, Tarski's relation algebra, graded modal*logic*, and the binary guarded ... include basic modal*logic*, its extension with counting modalities called graded modal*logic*(GM L), first-*order**logic*(by which we mean the collection of all first-*order*formulas*in*one free*variable*, ...##
###
Page 4581 of Mathematical Reviews Vol. , Issue 82k
[page]

1982
*
Mathematical Reviews
*

.; Rubin, M. 82k:03055

*Compact*fragments of higher*order**logic*. Mathematical*logic**in*Latin America ( Proc. IV Latin Amer. Sympos. Math.*Logic*, Santiago, 1978), pp. 219-238, Stud. ... Observe that these quantifiers are “first-*order*”*in*the sense that they operate on individuals x,,x,,--- only; the higher-*order**variables*occur only inside the quantifier itself. ...##
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First order logic, fixed point logic and linear order
[chapter]

1996
*
Lecture Notes in Computer Science
*

The

doi:10.1007/3-540-61377-3_37
fatcat:t2uyw6flffakna4vbbmeqp37zy
*Ordered*conjecture of Kolaitis and Vardi asks whether xed-point*logic*di ers from rst-*order**logic*on every*in*nite class of nite*ordered*structures. ... The*Ordered*conjecture of Kolaitis and Vardi asks whether fixed-point*logic*differs from first-*order**logic*on every infinite class of finite*ordered*structures. ... One of the most important tools*in*the analysis of the xed point*logics*is the bounded*variable**in*nitary*logic*L !*1*! . ...##
###
Biconditional Binary Decision Diagrams: A Novel Canonical Logic Representation Form

2014
*
IEEE Journal on Emerging and Selected Topics in Circuits and Systems
*

Empowered by reduction and

doi:10.1109/jetcas.2014.2361058
fatcat:odgpqsnwrncwbogbnbilvshdiq
*ordering*rules, BBDDs are remarkably*compact*and unique for a Boolean function. ... BBDDs are binary decision diagrams where the branching condition, and its associated*logic*expansion, is biconditional on two*variables*. ...*In*this work, we consider a novel*logic*expansion, called biconditional expansion, examining two*variables*per time rather than one,*in**order*to produce novel*compact*decision diagrams. ...##
###
Page 572 of Mathematical Reviews Vol. 24, Issue 6A
[page]

1962
*
Mathematical Reviews
*

The example illustrates very clearly the different cance of cut elimination

*in*the first-*order*and higher-*order*case ;*in*first-*order*a cut-free proof really proceeds from simpler to more complicated formulae ...*Logic*14 (1949), 159-166; MR 11, 487], and then using*compactness*to prove axiomatizability. ...##
###
Unlocking Controllable-Polarity Transistors Opportunities by Exclusive-OR and Majority Logic Synthesis

2014
*
2014 IEEE Computer Society Annual Symposium on VLSI
*

Nowadays, we observe a trend towards devices with an increased set of

doi:10.1109/isvlsi.2014.107
dblp:conf/isvlsi/GaillardonAM14
fatcat:bxephozbjrdu5icuxpeq5xf7uu
*logic*capabilities, i.e., with the ability to realize*in*a*compact*way specific*logic*operators as compared to the standard CMOS. ...*In*particular, controllable-polarity devices enable a native and*compact*realization of eXclusive-OR (XOR)-and MAJority (MAJ)-*logic*functions, and open a large panel of opportunities for future high-performance ... To correctly*order*a BBDD, one can impose a*variable**order*for PVs and follow the Chain*Variable**Order*(CVO) rule given*in*[11] to assign*variables*on the SVs. ...##
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Binary decision diagram to design balanced secure logic styles

2016
*
2016 IEEE 22nd International Symposium on On-Line Testing and Robust System Design (IOLTS)
*

An attack based on mutual information analysis (MIA) is applied to the AES S-boxes implemented

doi:10.1109/iolts.2016.7604710
dblp:conf/iolts/KimHPV16
fatcat:6wiiww5jjjdzrnpk266za467qy
*in*our novel secure*logic*style. ... This paper proposes binary decision diagrams (BDDs) to derive complex pull-down networks that fulfill all these requirements while being*compact*at the same time; it uses sense amplifier-based*logic*(SABL ...*In*the decision tree on the right side of Figure*1*, for instance, the*variables*are*ordered*as x2, x1, and x3. The*variable**ordering*is selected*in*view of the purpose of the BDD. ...##
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Page 8386 of Mathematical Reviews Vol. , Issue 2000m
[page]

2000
*
Mathematical Reviews
*

The author considers the bounded

*variable**logic*L*..,, the frag- ment of infinitary*logic*ZL...*in*which at most k*variable*symbols are permitted, and the*logic*C*,,,, obtained by adding arbitrary counting ... Bounded*variable**logics*are of interest because of their close relationship with fixed-point*logic*FP, the extension of first-*order**logic*by means of an inductive fixed-point operator. ...##
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Page 1475 of Mathematical Reviews Vol. 53, Issue 5
[page]

1977
*
Mathematical Reviews
*

n—2

*variables*, one of which is x2 or x, and this*variable*is then of*order*n—*1*. ... for f), then (a) the*variables*x,, x, are of*order*n—2 for f; (b) for each constant c that is admissible for x, the function S(%*1*, «++, X,)|x,;=c essentially depends on n—*1**variables*. ...##
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Translating Higher-Order Clauses to First-Order Clauses

2007
*
Journal of automated reasoning
*

Interactive provers typically use higher-

doi:10.1007/s10817-007-9085-y
fatcat:4uluysnq7rb7vjxzbcnvsgpcci
*order**logic*, while automatic provers typically use first-*order**logic*. ...*In**order*to integrate interactive provers with automatic ones, it is necessary to translate higher-*order*formulae to first-*order*form. The translation should ideally be both sound and practical. ... Omitting types yields a*compact*result, but the resulting proofs can be unsound : that is, meaningless*in*higher-*order**logic*. ...##
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Model Theory for C_p-theorists
[article]

2020
*
arXiv
*
pre-print

Iovino for

arXiv:2004.06537v1
fatcat:7ad4u4yxajfmxkgdg7xqp7jfva
*compact*continuous*logics*. ... We present a self-contained exposition of several interactions between continuous*logic*and C_p-theory which have applications to a classification problem involving Banach spaces not including c_0 or l ... We thank Vladimir Tkachuk for pointing us*in*the right direction toward finding the results we needed*in*C p -theory. ...
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