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

Luca Amaru, Pierre-Emmanuel Gaillardon, Giovanni De Micheli
2013 Design, Automation & Test in Europe Conference & Exhibition (DATE), 2013  
To exploit this opportunity 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.  ... 
doi:10.7873/date.2013.211 dblp:conf/date/AmaruGM13 fatcat:y2dcpzufsjgw5ayanvhn3cvefq

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.  ... 

Lindstrom theorems for fragments of first-order logic

Balder ten Cate, Johan van Benthem, Jouko Vaananen
2007 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)  
Examples of abstract 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,  ... 
doi:10.1109/lics.2007.29 dblp:conf/lics/CateBV07 fatcat:brerbh77lva7jecj4pqlj2m3de

PC-compactness, a necessary condition for the existence of sound and complete logics of partial correctness [chapter]

J. A. Bergstra, J. Tiuryn
1984 Lecture Notes in Computer Science  
A first 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.  ... 
doi:10.1007/3-540-12896-4_354 fatcat:4d66r3rjwrb4fpmjqak2uuujoa

Lindström theorems for fragments of first-order logic

Johan Van Benthem, Balder Ten Cate, Jouko Väänänen, Lawrence Moss
2009 Logical Methods in Computer Science  
Lindstr\"om theorems characterize 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,  ... 
doi:10.2168/lmcs-5(3:3)2009 fatcat:efpyabo6rrfhnexfqesab5fkby

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-orderin the sense that they operate on individuals x,,x,,--- only; the higher-order variables occur only inside the quantifier itself.  ... 

First order logic, fixed point logic and linear order [chapter]

Anuj Dawar, Steven Lindell, Scott Weinstein
1996 Lecture Notes in Computer Science  
The 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! .  ... 
doi:10.1007/3-540-61377-3_37 fatcat:t2uyw6flffakna4vbbmeqp37zy

Biconditional Binary Decision Diagrams: A Novel Canonical Logic Representation Form

Luca Amaru, Pierre-Emmanuel Gaillardon, Giovanni De Micheli
2014 IEEE Journal on Emerging and Selected Topics in Circuits and Systems  
Empowered by reduction and 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.  ... 
doi:10.1109/jetcas.2014.2361058 fatcat:odgpqsnwrncwbogbnbilvshdiq

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

Pierre-Emmanuel Gaillardon, Luca Gaetano Amaru, Giovanni De Micheli
2014 2014 IEEE Computer Society Annual Symposium on VLSI  
Nowadays, we observe a trend towards devices with an increased set of 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.  ... 
doi:10.1109/isvlsi.2014.107 dblp:conf/isvlsi/GaillardonAM14 fatcat:bxephozbjrdu5icuxpeq5xf7uu

Binary decision diagram to design balanced secure logic styles

Hyunmin Kim, Seokhie Hong, Bart Preneel, Ingrid Verbauwhede
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 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.  ... 
doi:10.1109/iolts.2016.7604710 dblp:conf/iolts/KimHPV16 fatcat:6wiiww5jjjdzrnpk266za467qy

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.  ... 

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.  ... 

Translating Higher-Order Clauses to First-Order Clauses

Jia Meng, Lawrence C. Paulson
2007 Journal of automated reasoning  
Interactive provers typically use higher-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.  ... 
doi:10.1007/s10817-007-9085-y fatcat:4uluysnq7rb7vjxzbcnvsgpcci

Model Theory for C_p-theorists [article]

Clovis Hamel, Franklin D. Tall
2020 arXiv   pre-print
Iovino for 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.  ... 
arXiv:2004.06537v1 fatcat:7ad4u4yxajfmxkgdg7xqp7jfva
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