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Explaining SAT Solving Using Causal Reasoning.
Jiong Yang, Arijit Shaw, Teodora Baluta, Mate Soos and Kuldeep S. Meel.
In Proceedings of the International Conference on Theory and Applications of Satisfiability Testing (SAT), July 2023.
The past three decades have witnessed notable success in designing efficient SAT solvers, with modern solvers capable of solving industrial benchmarks containing millions of variables in just a few seconds. The success of modern SAT solvers owes to the widely-used CDCL algorithm, which lacks comprehensive theoretical investigation. Furthermore, it has been observed that CDCL solvers still struggle to deal with specific classes of benchmarks comprising only hundreds of variables, which contrasts with their widespread use in real-world applications. Consequently, there is an urgent need to uncover the inner workings of these seemingly weak yet powerful black boxes. In this paper, we present a first step towards this goal by introducing an approach called CausalSAT, which employs causal reasoning to gain insights into the functioning of modern SAT solvers. CausalSAT initially generates observational data from the execution of SAT solvers and learns a structured graph representing the causal relationships between the components of an SAT solver. Subsequently, given a query such as whether a clause with low literals blocks distance (LBD) has a higher clause utility, CausalSAT calculates the causal effect of LBD on clause utility and provides an answer to the question. We utilize CausalSAT to quantitatively verify hypotheses previously regarded as "rules of thumb" or empirical findings, such as the query above or the notion that clauses with high LBD experience a rapid drop in utility over time. Moreover, CausalSAT can address previously unexplored questions, like which branching heuristic results in greater clause utility in order to study the relationship between branching and clause management. Experimental evaluations using practical benchmarks demonstrate that CausalSAT effectively fits the data, verifies four "rules of thumb", and provides answers to three questions closely related to implementing modern solvers.
@inproceedings{YSBSM23,
author={
Yang, Jiong and Shaw, Arijit and Baluta, Teodora and Soos, Mate and Meel,
Kuldeep S.
},
title={Explaining SAT Solving Using Causal Reasoning},
abstract={
The past three decades have witnessed notable success in designing efficient
SAT solvers,
with modern solvers capable of solving industrial benchmarks containing
millions of variables in
just a few seconds. The success of modern SAT solvers owes to the
widely-used CDCL algorithm, which
lacks comprehensive theoretical investigation. Furthermore, it has been
observed that CDCL solvers still
struggle to deal with specific classes of benchmarks comprising only
hundreds of variables, which contrasts
with their widespread use in real-world applications. Consequently, there is
an urgent need to uncover the
inner workings of these seemingly weak yet powerful black boxes.
In this paper, we present a first step towards this goal by introducing an
approach called
CausalSAT, which employs causal reasoning to gain insights into the
functioning of modern
SAT solvers. CausalSAT initially generates observational data from the
execution of SAT solvers
and learns a structured graph representing the causal relationships between
the components of an
SAT solver. Subsequently, given a query such as whether a clause with low
literals blocks distance
(LBD) has a higher clause utility, CausalSAT calculates the causal effect of
LBD on clause utility
and provides an answer to the question. We utilize CausalSAT to
quantitatively verify hypotheses
previously regarded as "rules of thumb" or empirical findings, such as the
query above or the notion
that clauses with high LBD experience a rapid drop in utility over time.
Moreover, CausalSAT can
address previously unexplored questions, like which branching heuristic
results in greater clause
utility in order to study the relationship between branching and clause
management. Experimental
evaluations using practical benchmarks demonstrate that CausalSAT
effectively fits the data,
verifies four "rules of thumb", and provides answers to three questions
closely related to implementing modern solvers.
},
year={2023},
month=jul,
booktitle=SAT,
bib2html_pubtype={Refereed Conference},
bib2html_rescat={Solver Engineering},
bib2html_dl_pdf={https://arxiv.org/pdf/2306.06294.pdf},
}
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