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Skolem Functions for Factored Formulas
[article]

2015
*
arXiv
*
pre-print

We present a new CEGAR style algorithm

arXiv:1508.05497v2
fatcat:lbugq7cfpjfqtonixhbn7fniha
*for*generating*Skolem**functions*from*factored*propositional*formulas*. ... Given a propositional*formula*F(x,y), a*Skolem**function**for*x is a*function*\Psi(y), such that substituting \Psi(y)*for*x in F gives a*formula*semantically equivalent to \exists F. ... CONCLUSION AND FUTURE WORK We presented a CEGAR algorithm*for*generating*Skolem**functions*from*factored*propositional*formulas*. ...##
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Skolem functions for factored formulas

2015
*
2015 Formal Methods in Computer-Aided Design (FMCAD)
*

Solution: Find

doi:10.1109/fmcad.2015.7542255
fatcat:2lbap6jvbbfsfgiyvmstppdvma
*Skolem**function**for*the input variables X in: 2. Generate*Skolem**functions*matching a given template. ∧ i NotCovered i (X, Y ). ... assumption Composition based approaches -Quantifier elimination via*functional*composition by Jiang [Jia09] -Techniques in Symbolic model checking by Trivedi [Tri03] -Work well*for*small-sized*formulas*... . · · · · · · -*Skolem**functions*are in*factored*form: How to avoid such blowup . . . . . . · · · · · · -*Skolem**functions*are in*factored*form: ψ i = ∧ψ k i ...##
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What's hard about Boolean Functional Synthesis
[article]

2018
*
arXiv
*
pre-print

In this paper, we first show that unless some hard conjectures in complexity theory are falsified, Boolean

arXiv:1804.05507v2
fatcat:fqne5bnv7jf3zn7aitenhb6n6y
*functional*synthesis must necessarily generate exponential-sized*Skolem**functions*, thereby requiring ... We present a two-phase algorithm*for*Boolean*functional*synthesis, where the first phase is efficient both in terms of time and sizes of synthesized*functions*, and solves an overwhelming majority of benchmarks ... The*function*ψ i is called a*Skolem**function**for*x i in F , and Ψ = (ψ 1 , . . . ψ n ) is called a*Skolem**function*vector*for*X in F . ...##
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What's Hard About Boolean Functional Synthesis?
[chapter]

2018
*
Lecture Notes in Computer Science
*

In this paper, we first show that unless some hard conjectures in complexity theory are falsified, Boolean

doi:10.1007/978-3-319-96145-3_14
fatcat:ws2spinhwbeljamzk5cjti634a
*functional*synthesis must generate large*Skolem**functions*in the worst-case. ... Detailed experimental evaluation shows our algorithm to perform better than other techniques*for*a large number of benchmarks. ... We also thank the anonymous reviewers*for*insightful comments. ...##
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Translation of resolution proofs into short first-order proofs without choice axioms

2005
*
Information and Computation
*

We present a way of transforming a resolution-style proof containing

doi:10.1016/j.ic.2004.10.011
fatcat:xt4buqzzf5hhvpvyvpk47vddmq
*Skolemization*into a natural deduction proof without*Skolemization*. ... I thank Marc Bezem*for*discussions on the subject of this paper and Dimitri Hendriks*for*the pleasant cooperation in [6] , which is one of the roots of the current paper. ... Acknowledgments It was due to a question asked by Georg Moser during the Deduktionstreffen 2002 in Freiburg that I started thinking about the problem of eliminating*Skolemization*without eliminating cuts ...##
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Translation of Resolution Proofs into Short First-Order Proofs without Choice Axioms
[chapter]

2003
*
Lecture Notes in Computer Science
*

The clausal proof can contain resolution, paramodulation,

doi:10.1007/978-3-540-45085-6_33
fatcat:ih352adeizfhzoz3ge5to6wghe
*factoring*) into a purely first-order proof of the same*formula*. ... I present a way of transforming a resolution proof on the first-order level (The CNF-transformation can contain*Skolemization*, subformula replacements. ... A*Skolem**function*f originates from*Skolemizing*some*formula*∀x 1 · · · x n ∃y A(x 1 , . . . , x n , y). Simply take A as the serial relation*for*f : 1. ...##
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Manthan: A Data-Driven Approach for Boolean Function Synthesis
[chapter]

2020
*
Lecture Notes in Computer Science
*

Manthan views

doi:10.1007/978-3-030-53291-8_31
fatcat:xvkvq2axajfmhbaofayqk6laqq
*functional*synthesis as a classification problem, relying on advances in constrained sampling*for*data generation, and advances in automated reasoning*for*a novel proof-guided refinement ... Motivated by the progress in machine learning, we propose Manthan, a novel data-driven approach to Boolean*functional*synthesis. ... We are grateful to Mate Soos*for*tweaking BiasGen to support Manthan. We are indebted to S. ...##
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Manthan: A Data Driven Approach for Boolean Function Synthesis
[article]

2020
*
arXiv
*
pre-print

Manthan views

arXiv:2005.06922v1
fatcat:mcocntrshzbq3fhys2vfuj2hdu
*functional*synthesis as a classification problem, relying on advances in constrained sampling*for*data generation, and advances in automated reasoning*for*a novel proof-guided refinement ... Motivated by the progress in machine learning, we propose Manthan, a novel data-driven approach to Boolean*functional*synthesis. ... We are grateful to Mate Soos*for*tweaking BiasGen to support Manthan. We are indebted to S. ...##
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Automated reasoning with quantified formulae

2009
*
Proceedings of the Eighth International Workshop on the ACL2 Theorem Prover and its Applications - ACL2 '09
*

We present an ACL2 framework that employs tables, computed hints and clause processing to identify quantified

doi:10.1145/1637837.1637855
fatcat:fadir2w2vrbhpduvcpawykveay
*formulae*and to*skolemize*or instantiate them when possible. ... ACL2 allows users to define predicates whose logical behavior mimics that of universally or existentially quantified*formulae*. Proof support*for*such quantification, however, is quite limited. ... It is possible*for**skolemization*to prepare the way*for*induction by replacing a*function*call with a symbol. ...##
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Synthesis from Assume-Guarantee Contracts using Skolemized Proofs of Realizability
[article]

2017
*
arXiv
*
pre-print

The proof of re- alizability is performed over a set of forall-exists

arXiv:1610.05867v3
fatcat:6bs6utnisvbujfdck6cetz2sae
*formulas*, and synthesis is per- formed by extracting*Skolem**functions*witnessing the existential quan- tification. ... These*Skolem**functions*can then be combined into an imple- mentation. ... Given a*formula*∃ . (⃗, ), a*Skolem**function**for*, sk (⃗) is a*function*such that ∃ . (⃗, ) ⇐⇒ (⃗, sk (⃗)). ...##
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Skolem functions of arithmetical sentences

2003
*
Information and Computation
*

We define the

doi:10.1016/s0890-5401(03)00085-3
fatcat:gbmmulf4fjf33cqhfy376tdafi
*Skolem**function*f (x)*for*∀x∃y ψ(x, y) as follows.*For*any a in N (or Z) let f (a) be the least (or least absolute value of) b such that ψ(a, b) is true in N (or Z). ...*For*every arithmetical sentence ∀x∃y∀z ψ(x, y, z) true in N (or Z) there is a polynomial g(x) over Z such that the corresponding*Skolem**function*f (x) < g(|x|)*for*any x in N (or Z). ...*Skolem**functions*Suppose that ∀x∃y φ(x, y) is true in N (or Z). We define the*Skolem**function*f (x)*for*∀x∃y φ(x, y) as follows. ...##
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A Normal Form Characterization for Efficient Boolean Skolem Function Synthesis
[article]

2021
*
arXiv
*
pre-print

Boolean

arXiv:2104.14098v2
fatcat:cmhxttn3xze5fhl6yaskdnwauq
*Skolem**function*synthesis concerns synthesizing outputs as Boolean*functions*of inputs such that a relational specification between inputs and outputs is satisfied. ... Thus, SAUNF provides the right trade-off in knowledge representation*for*Boolean*functional*synthesis. ... Finding*Skolem**functions**for*X 1 and X 2 in terms of I effectively asks us to solve the (n-bit)*factorization*problem. ...##
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Distributed agent-based automated theorem proving in order-sorted first-order logic
[article]

2016
*
arXiv
*
pre-print

In this paper we provide a refutation-complete report procedure

arXiv:1609.02320v1
fatcat:yyfnhez6fncbrjxyte5opeb4ka
*for*automated theorem proving in order-sorted first-order logic in a subclass of distributed agent-based networks. ...*Function*symbols h, i, and j in Figure 1 are*Skolem*symbols employed*for*the*Skolemization*procedure. ... Since*functions*h and i are acceptable*for*our un-*Skolemization*procedure (see Appendix A), agent y can report the un-*Skolemized*Σ-*formulae*∀c 1 :C∃p 1 :P . E(c 1 :C p 1 :P ) and ∀s 1 :S∃p 2 :P . ...##
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Automated Proof Construction in Type Theory Using Resolution
[chapter]

2000
*
Lecture Notes in Computer Science
*

Abstract We present a way of transforming a resolution-style proof containing

doi:10.1007/10721959_10
fatcat:oppgj6ht65bkvkwfudmxktx74a
*Skolemization*into a natural deduction proof without*Skolemization*. ... This paper discusses the problem of how to transform a firstorder*formula*into clausal normal form, and to simultaneously construct a proof that the clausal normal form is correct. ... Pliuskevicius*for*insisting on a complexity analysis. ...##
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Incremental Determinization
[chapter]

2016
*
Lecture Notes in Computer Science
*

The algorithm incrementally adds new constraints to the

doi:10.1007/978-3-319-40970-2_23
fatcat:ytj7npoqarcl5mtrbmjoakkgii
*formula*until the constraints describe a unique*Skolem**function*-or until the absence of a*Skolem**function*is detected. ... We present the algorithm in analogy to search algorithms*for*SAT and explain how propagation, decisions, and conflicts are lifted from values to*Skolem**functions*. ... We thank our anonymous reviewers*for*their comments and Marcell Vazquez-Chanlatte, Leander Tentrup, Ashutosh Trivedi, and Christoph Wintersteiger*for*fruitful discussions on this work. ...
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