979 research outputs found
Generating clause sequences of a CNF formula
Given a CNF formula with clauses and variables
, a truth assignment of
leads to a clause sequence
where if clause evaluates to under assignment ,
otherwise . The set of all possible clause sequences carries a lot
of information on the formula, e.g. SAT, MAX-SAT and MIN-SAT can be encoded in
terms of finding a clause sequence with extremal properties.
We consider a problem posed at Dagstuhl Seminar 19211 "Enumeration in Data
Management" (2019) about the generation of all possible clause sequences of a
given CNF with bounded dimension. We prove that the problem can be solved in
incremental polynomial time. We further give an algorithm with polynomial delay
for the class of tractable CNF formulas. We also consider the generation of
maximal and minimal clause sequences, and show that generating maximal clause
sequences is NP-hard, while minimal clause sequences can be generated with
polynomial delay.Comment: 9 page
Incremental QBF Solving
We consider the problem of incrementally solving a sequence of quantified
Boolean formulae (QBF). Incremental solving aims at using information learned
from one formula in the process of solving the next formulae in the sequence.
Based on a general overview of the problem and related challenges, we present
an approach to incremental QBF solving which is application-independent and
hence applicable to QBF encodings of arbitrary problems. We implemented this
approach in our incremental search-based QBF solver DepQBF and report on
implementation details. Experimental results illustrate the potential benefits
of incremental solving in QBF-based workflows.Comment: revision (camera-ready, to appear in the proceedings of CP 2014,
LNCS, Springer
Automated Benchmarking of Incremental SAT and QBF Solvers
Incremental SAT and QBF solving potentially yields improvements when
sequences of related formulas are solved. An incremental application is usually
tailored towards some specific solver and decomposes a problem into incremental
solver calls. This hinders the independent comparison of different solvers,
particularly when the application program is not available. As a remedy, we
present an approach to automated benchmarking of incremental SAT and QBF
solvers. Given a collection of formulas in (Q)DIMACS format generated
incrementally by an application program, our approach automatically translates
the formulas into instructions to import and solve a formula by an incremental
SAT/QBF solver. The result of the translation is a program which replays the
incremental solver calls and thus allows to evaluate incremental solvers
independently from the application program. We illustrate our approach by
different hardware verification problems for SAT and QBF solvers.Comment: camera-ready version (8 pages + 2 pages appendix), to appear in the
proceedings of the 20th International Conference on Logic for Programming,
Artificial Intelligence and Reasoning (LPAR), LNCS, Springer, 201
Generating Schemata of Resolution Proofs
Two distinct algorithms are presented to extract (schemata of) resolution
proofs from closed tableaux for propositional schemata. The first one handles
the most efficient version of the tableau calculus but generates very complex
derivations (denoted by rather elaborate rewrite systems). The second one has
the advantage that much simpler systems can be obtained, however the considered
proof procedure is less efficient
The use of data-mining for the automatic formation of tactics
This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques
Redundancy in Logic III: Non-Mononotonic Reasoning
Results about the redundancy of circumscriptive and default theories are
presented. In particular, the complexity of establishing whether a given theory
is redundant is establihsed.Comment: minor correction
The Complexity of Planning Problems With Simple Causal Graphs
We present three new complexity results for classes of planning problems with
simple causal graphs. First, we describe a polynomial-time algorithm that uses
macros to generate plans for the class 3S of planning problems with binary
state variables and acyclic causal graphs. This implies that plan generation
may be tractable even when a planning problem has an exponentially long minimal
solution. We also prove that the problem of plan existence for planning
problems with multi-valued variables and chain causal graphs is NP-hard.
Finally, we show that plan existence for planning problems with binary state
variables and polytree causal graphs is NP-complete
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