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On truth-table reducibility to SAT

1991
*
Information and Computation
*

We show that polynomial time

doi:10.1016/0890-5401(91)90075-d
fatcat:rgymrlwjirbwrhdhdiclwayrga
*truth*-*table**reducibility*via Boolean circuits*to**SAT*is the same as logspace*truth*-*table**reducibility*via Boolean formulas*to**SAT*and the same as logspace Turing*reducibility*... We give an oracle relative*to*which ∆ p 2 is not equal*to*the class of predicates polynomial time*truth*-*table**reducible**to**SAT*. ...*to**SAT*, • A is polynomial time, Boolean formula*truth*-*table**reducible**to**SAT*, • A is logspace, Boolean formula*truth*-*table**reducible**to**SAT*, • A is logspace, Turing*reducible**to**SAT*, ...##
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On truth-table reducibility to SAT and the difference hierarchy over NP

1988
*
[1988] Proceedings. Structure in Complexity Theory Third Annual Conference
*

We show that polynomial time

doi:10.1109/sct.1988.5282
dblp:conf/coco/BussH88
fatcat:tvrzntst7zggbb44g743uguysa
*truth*-*table**reducibility*via Boolean circuits*to**SAT*is the same as log space*truth*-*table**reducibility*via Boolean formulas*to**SAT*and the same as log space Turing*reducibility*... Finally, we show that the infinite difference hierarchy over NP is equal*to*∆ p 2 and give an oracle oracle separating ∆ p 2 from the class of predicates polynomial time*truth*-*table**reducible**to**SAT*. ... polynomial time, Boolean formula*truth*-*table**reducible**to**SAT*, • A is log space, Boolean formula*truth*-*table**reducible**to**SAT*, • A is log space, Turing*reducible**to**SAT*, • A is definable by a Σ b 2 ∩ ...##
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Probabilistic Autoreductions
[chapter]

2016
*
Lecture Notes in Computer Science
*

autoreducible with respect

doi:10.1007/978-3-662-49192-8_34
fatcat:mtudxhfu35hnlmuya5g2o562mm
*to*the BPP*truth*-*table*reductions. ... This generalizes the result by Buhrman et. al. (2000) that*truth*-*table*-complete sets for NP are probabilistically*truth*-*table*autoreducible*to*multiple classes of higher complexity although for a weaker ... Now let L a be a BPP*truth*-*table*-complete set for Σ P,tt k for k ≥ 1. Then L a*reduces**to**SAT*(k),tt via a many-*one*reduction f that does not use any oracle. ...##
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On the Power of Positive Turing Reductions
[article]

1999
*
arXiv
*
pre-print

In particular, positive Turing reduction

arXiv:cs/9906028v1
fatcat:4khays6ih5hxbckl5squupthti
*to*DP already yields all (and only) sets Turing*reducibility**to*NP. Thus, positive Turing and Turing*reducibility**to*DP yield the same class. ... In the early 1980s, Selman's seminal work*on*positive Turing reductions showed that positive Turing reduction*to*NP yields no greater computational power than NP itself. ... Acknowledgments For helpful conversations and suggestions, I am very grateful*to*Lane Hemaspaandra, Harald Hempel, Jörg Rothe, and Gerd Wechsung. ...##
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Complexity-Restricted Advice Functions

1994
*
SIAM journal on computing (Print)
*

As a consequence, we show that every set that is nondeterministically

doi:10.1137/s0097539791200351
fatcat:3oqdkrhzdzhrrervnymtl44nwy
*truth*-*table**reducible**to**SAT*in the sense of Rich 35] is already deterministically*truth*-*table**reducible**to**SAT*. ... We also investigate the e ect of allowing advice functions of limited complexity*to*depend*on*the input rather than*on*the input's length. ... For helpful conversations and suggestions*on*this work we are grateful*to*V. Arvind, L. Hemachandra, and U. Sch*oning*. We also thank the two referees for their valuable suggestions. ...##
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Learning Finite Linear Temporal Logic Specifications with a Specialized Neural Operator
[article]

2021
*
arXiv
*
pre-print

Then, it discretizes the activations and extracts the

arXiv:2111.04147v2
fatcat:nra26bckifgbxkpgt2zlvryb4q
*truth**table*represented by the learned weights. This*truth**table*is converted*to*symbolic form and returned as the learned formula. ... Experiments*on*randomly generated 𝖫𝖳𝖫_f formulas show Neural𝖫𝖳𝖫_f scales*to*larger formula sizes than existing approaches and maintains high accuracy even in the presence of noise. ... They*reduce*the LTL f learning problem*to**SAT*, but their method does not scale well*to*larger formula sizes or trace sets. ...##
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The difference and truth-table hierarchies for NP

1987
*
RAIRO - Theoretical Informatics and Applications
*

Note that m dépends

doi:10.1051/ita/1987210404191
fatcat:u6ragzrbbndktbjjnoveibir74
*on*x. (ii) A set A is polynomial-time fc-bounded*truth*-*table**reducible**to*B(A^l_ tt B) iff A<** t B via a function ƒ having at most (fc-h l)-tuples as values. ... (iii) A set A is polynomial-time bounded*truth*-*table**reducible**to*B(A^l tt B) iff ASk-tt B f or some fc^l. (iv) For a class of sets C and a*reducibility*a let a(C) = {>! ...##
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Exploiting symmetry in SAT-based boolean matching for heterogeneous FPGA technology mapping

2007
*
Computer-Aided Design (ICCAD), IEEE International Conference on
*

While the most recent work obtained up

doi:10.1109/iccad.2007.4397289
dblp:conf/iccad/HuSMH07
fatcat:rb6o4j46gngnbczbltv7t7zzzm
*to*13x speedup, we achieve up*to*200x speedup, when both are compared*to*the original*SAT*-BM algorithm. * This paper is partially supported by NSF grant CCR-0306682 ... Address comments*to*lhe@ee.ucla.edu. ... A K-LUT device consists of K inputs,*one*output, and 2 K configuration bits that serve as*truth**table*entries. ...##
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Page 10 of Mathematical Reviews Vol. , Issue 92c
[page]

1992
*
Mathematical Reviews
*

In particular, the authors show that polynomial time

*truth*-*table**reducibility*via Boolean circuits*to**SAT*is the same as logspace*truth*-*table**reducibility*via Boolean formulas*to**SAT*and the same as logspace ... They give an oracle relative*to*which A} is not equal*to*the class of predicates polynomial time*truth*-*table**reducible**to**SAT*. ...##
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Heuristic NPN Classification for Large Functions Using AIGs and LEXSAT
[chapter]

2016
*
Lecture Notes in Computer Science
*

So far, these heuristics have been implemented using the function's

doi:10.1007/978-3-319-40970-2_14
fatcat:dgkutenqzrfm7jj76cd4yiinom
*truth**table*representation, and therefore do not scale for functions exceeding 16 variables. ... Two Boolean functions are NPN equivalent if*one*can be obtained from the other by negating inputs, permuting inputs, or negating the output. ... The smallest*truth**table*is the*one*with the smallest integer value, when considering the*truth**table*as a binary number. ...##
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Assimilation of Satellite Infrared Radiances and Doppler Radar Observations during a Cool Season Observing System Simulation Experiment

2013
*
Monthly Weather Review
*

Comparison with the high-resolution "

doi:10.1175/mwr-d-12-00267.1
fatcat:v5eajzk72vg4hedr7qz45mxvkm
*truth*" simulation indicates that the joint assimilation of satellite and radar observations*reduces*errors in cloud properties compared*to*the case in which only conventional ... observations*on*the analysis accuracy of a cool season extratropical cyclone. ... We would also like*to*thank the three anonymous reviewers who provided comments that improved the overall quality of this manuscript. ...##
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Exploiting Symmetries to Speed Up SAT-Based Boolean Matching for Logic Synthesis of FPGAs

2008
*
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
*

In this paper, we leverage symmetries present in both Boolean functions and target FPGA architectures

doi:10.1109/tcad.2008.2003272
fatcat:3sp5jacv4bahrnxyhkyxz2pdvu
*to*prune the solution space, and we also propose some techniques*to**reduce*the replication runtime ... Experiment shows that our*SAT*-BM*reduces*runtime by 226× compared with the original*SAT*-BM algorithm, making*SAT*-BM more practical. ... In our implementation, we start with a subset containing clauses representing*one**truth**table*entry. ...##
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A Critique of a Polynomial-time SAT Solver Devised by Sergey Gubin
[article]

2008
*
arXiv
*
pre-print

Because 3-

arXiv:0804.2699v1
fatcat:7m77whlldbcjrhbxwpkb2kzkc4
*SAT*is NP-complete, the algorithm would have implied P = NP, had it been correct. Additionally, this paper refutes the correctness of his polynomial-time reduction of*SAT**to*2-*SAT*. ... Gubin introduces the algorithm using 3-*SAT*and eventually expands it*to*accept a broad range of forms of the Boolean satisfiability problem. ... The matrix C 2,3 is constructed by representing the*truth**table*of clause c 2*on*the vertical axis, and the*truth**table*of clause c 3*on*the horizontal axis. ...##
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Learning Reductions to Sparse Sets
[chapter]

2013
*
Lecture Notes in Computer Science
*

We furthermore show that if

doi:10.1007/978-3-642-40313-2_23
fatcat:ocm23fh4lzfyppn3w2qp5q4nyq
*Sat*disjunctive*truth*-*table*(or majority*truth*-*table*)*reduces**to*a sparse set then*Sat*≤ p m LT1 and hence a collapse of PH*to*P NP also follows. ... We continue the work of Agrawal and Arvind [1] who study the consequences of*Sat*being many-*one**reducible**to*functions computable by non-uniform circuits consisting of a single weighted threshold gate. ... 2 j=1C(s)jC(y)j. dtt SPARSE ...*truth*-*table*reductions*to*sparse sets are powerful enough*to*simulate bounded*truth*-*table*reductions*to*sparse sets [2] . ...##
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Towards Faster Reasoners By Using Transparent Huge Pages
[article]

2020
*
arXiv
*
pre-print

In this work, we present an approach

arXiv:2004.14378v1
fatcat:medbvwxdijgapccue4g5a5fec4
*to**reduce*the runtime of AR tools by 10%*on*average and up*to*20% for long running tasks. ...*To*back up the claimed speed-up, we present experimental results for tools that are commonly used in the AR community, including the domains ASP, BMC, MaxSAT,*SAT*, and SMT. ... We call a clause C unit if τ assigns all but*one*literal*to*0. A*truth*assignment τ is satisfying if for each clause C ∈ F , the*truth*assignment τ satisfies C. Why*SAT*solvers are fast? ...
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