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On truth-table reducibility to SAT

Samuel R. Buss, Louise Hay
1991 Information and Computation  
We 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 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,  ... 
doi:10.1016/0890-5401(91)90075-d fatcat:rgymrlwjirbwrhdhdiclwayrga

On truth-table reducibility to SAT and the difference hierarchy over NP

S.R. Buss, L. Hay
1988 [1988] Proceedings. Structure in Complexity Theory Third Annual Conference  
We show that polynomial time 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 ∩  ... 
doi:10.1109/sct.1988.5282 dblp:conf/coco/BussH88 fatcat:tvrzntst7zggbb44g743uguysa

Probabilistic Autoreductions [chapter]

Liyu Zhang, Chen Yuan, Haibin Kan
2016 Lecture Notes in Computer Science  
autoreducible with respect 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.  ... 
doi:10.1007/978-3-662-49192-8_34 fatcat:mtudxhfu35hnlmuya5g2o562mm

On the Power of Positive Turing Reductions [article]

Edith Hemaspaandra
1999 arXiv   pre-print
In particular, positive Turing reduction 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.  ... 
arXiv:cs/9906028v1 fatcat:4khays6ih5hxbckl5squupthti

Complexity-Restricted Advice Functions

Johannes Köbler, Thomas Thierauf
1994 SIAM journal on computing (Print)  
As a consequence, we show that every set that is nondeterministically 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.  ... 
doi:10.1137/s0097539791200351 fatcat:3oqdkrhzdzhrrervnymtl44nwy

Learning Finite Linear Temporal Logic Specifications with a Specialized Neural Operator [article]

Homer Walke, Daniel Ritter, Carl Trimbach, Michael Littman
2021 arXiv   pre-print
Then, it discretizes the activations and extracts the 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.  ... 
arXiv:2111.04147v2 fatcat:nra26bckifgbxkpgt2zlvryb4q

The difference and truth-table hierarchies for NP

Johannes Köbler, Uwe Schöning, Klaus W. Wagner
1987 RAIRO - Theoretical Informatics and Applications  
Note that m dépends 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) = {>!  ... 
doi:10.1051/ita/1987210404191 fatcat:u6ragzrbbndktbjjnoveibir74

Exploiting symmetry in SAT-based boolean matching for heterogeneous FPGA technology mapping

Yu Hu, Victor Shih, Rupak Majumdar, Lei He
2007 Computer-Aided Design (ICCAD), IEEE International Conference on  
While the most recent work obtained up 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.  ... 
doi:10.1109/iccad.2007.4397289 dblp:conf/iccad/HuSMH07 fatcat:rb6o4j46gngnbczbltv7t7zzzm

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.  ... 

Heuristic NPN Classification for Large Functions Using AIGs and LEXSAT [chapter]

Mathias Soeken, Alan Mishchenko, Ana Petkovska, Baruch Sterin, Paolo Ienne, Robert K. Brayton, Giovanni De Micheli
2016 Lecture Notes in Computer Science  
So far, these heuristics have been implemented using the function's 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.  ... 
doi:10.1007/978-3-319-40970-2_14 fatcat:dgkutenqzrfm7jj76cd4yiinom

Assimilation of Satellite Infrared Radiances and Doppler Radar Observations during a Cool Season Observing System Simulation Experiment

Thomas A. Jones, Jason A. Otkin, David J. Stensrud, Kent Knopfmeier
2013 Monthly Weather Review  
Comparison with the high-resolution "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.  ... 
doi:10.1175/mwr-d-12-00267.1 fatcat:v5eajzk72vg4hedr7qz45mxvkm

Exploiting Symmetries to Speed Up SAT-Based Boolean Matching for Logic Synthesis of FPGAs

Yu Hu, V. Shih, R. Majumdar, Lei He
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 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.  ... 
doi:10.1109/tcad.2008.2003272 fatcat:3sp5jacv4bahrnxyhkyxz2pdvu

A Critique of a Polynomial-time SAT Solver Devised by Sergey Gubin [article]

Ian Christopher, Dennis Huo, Bryan Jacobs
2008 arXiv   pre-print
Because 3-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.  ... 
arXiv:0804.2699v1 fatcat:7m77whlldbcjrhbxwpkb2kzkc4

Learning Reductions to Sparse Sets [chapter]

Harry Buhrman, Lance Fortnow, John M. Hitchcock, Bruno Loff
2013 Lecture Notes in Computer Science  
We furthermore show that if 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] .  ... 
doi:10.1007/978-3-642-40313-2_23 fatcat:ocm23fh4lzfyppn3w2qp5q4nyq

Towards Faster Reasoners By Using Transparent Huge Pages [article]

Johannes K. Fichte, Norbert Manthey, Julian Stecklina, André Schidler
2020 arXiv   pre-print
In this work, we present an approach 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?  ... 
arXiv:2004.14378v1 fatcat:medbvwxdijgapccue4g5a5fec4
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