3,151 research outputs found
Probabilistic Inference Modulo Theories
We present SGDPLL(T), an algorithm that solves (among many other problems)
probabilistic inference modulo theories, that is, inference problems over
probabilistic models defined via a logic theory provided as a parameter
(currently, propositional, equalities on discrete sorts, and inequalities, more
specifically difference arithmetic, on bounded integers). While many solutions
to probabilistic inference over logic representations have been proposed,
SGDPLL(T) is simultaneously (1) lifted, (2) exact and (3) modulo theories, that
is, parameterized by a background logic theory. This offers a foundation for
extending it to rich logic languages such as data structures and relational
data. By lifted, we mean algorithms with constant complexity in the domain size
(the number of values that variables can take). We also detail a solver for
summations with difference arithmetic and show experimental results from a
scenario in which SGDPLL(T) is much faster than a state-of-the-art
probabilistic solver.Comment: Submitted to StarAI-16 workshop as closely revised version of
IJCAI-16 pape
SAT-Based Synthesis Methods for Safety Specs
Automatic synthesis of hardware components from declarative specifications is
an ambitious endeavor in computer aided design. Existing synthesis algorithms
are often implemented with Binary Decision Diagrams (BDDs), inheriting their
scalability limitations. Instead of BDDs, we propose several new methods to
synthesize finite-state systems from safety specifications using decision
procedures for the satisfiability of quantified and unquantified Boolean
formulas (SAT-, QBF- and EPR-solvers). The presented approaches are based on
computational learning, templates, or reduction to first-order logic. We also
present an efficient parallelization, and optimizations to utilize reachability
information and incremental solving. Finally, we compare all methods in an
extensive case study. Our new methods outperform BDDs and other existing work
on some classes of benchmarks, and our parallelization achieves a super-linear
speedup. This is an extended version of [5], featuring an additional appendix.Comment: Extended version of a paper at VMCAI'1
From Quantified CTL to QBF
QCTL extends the temporal logic CTL with quantifications over atomic propositions. This extension is known to be very expressive: QCTL allows us to express complex properties over Kripke structures (it is as expressive as MSO). Several semantics exist for the quantifications: here, we work with the structure semantics, where the extra propositions label the Kripke structure (and not its execution tree), and the model-checking problem is known to be PSPACE-complete in this framework. We propose a model-checking algorithm for QCTL based on a reduction to QBF. We consider several reduction strategies, and we compare them with a prototype (based on the SMT-solver Z3) on several examples
Conformant Planning as a Case Study of Incremental QBF Solving
We consider planning with uncertainty in the initial state as a case study of
incremental quantified Boolean formula (QBF) solving. We report on experiments
with a workflow to incrementally encode a planning instance into a sequence of
QBFs. To solve this sequence of incrementally constructed QBFs, we use our
general-purpose incremental QBF solver DepQBF. Since the generated QBFs have
many clauses and variables in common, our approach avoids redundancy both in
the encoding phase and in the solving phase. Experimental results show that
incremental QBF solving outperforms non-incremental QBF solving. Our results
are the first empirical study of incremental QBF solving in the context of
planning and motivate its use in other application domains.Comment: added reference to extended journal article; revision (camera-ready,
to appear in the proceedings of AISC 2014, volume 8884 of LNAI, Springer
DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL
We present the latest major release version 6.0 of the quantified Boolean
formula (QBF) solver DepQBF, which is based on QCDCL. QCDCL is an extension of
the conflict-driven clause learning (CDCL) paradigm implemented in state of the
art propositional satisfiability (SAT) solvers. The Q-resolution calculus
(QRES) is a QBF proof system which underlies QCDCL. QCDCL solvers can produce
QRES proofs of QBFs in prenex conjunctive normal form (PCNF) as a byproduct of
the solving process. In contrast to traditional QCDCL based on QRES, DepQBF 6.0
implements a variant of QCDCL which is based on a generalization of QRES. This
generalization is due to a set of additional axioms and leaves the original
Q-resolution rules unchanged. The generalization of QRES enables QCDCL to
potentially produce exponentially shorter proofs than the traditional variant.
We present an overview of the features implemented in DepQBF and report on
experimental results which demonstrate the effectiveness of generalized QRES in
QCDCL.Comment: 12 pages + appendix; to appear in the proceedings of CADE-26, LNCS,
Springer, 201
On QBF Proofs and Preprocessing
QBFs (quantified boolean formulas), which are a superset of propositional
formulas, provide a canonical representation for PSPACE problems. To overcome
the inherent complexity of QBF, significant effort has been invested in
developing QBF solvers as well as the underlying proof systems. At the same
time, formula preprocessing is crucial for the application of QBF solvers. This
paper focuses on a missing link in currently-available technology: How to
obtain a certificate (e.g. proof) for a formula that had been preprocessed
before it was given to a solver? The paper targets a suite of commonly-used
preprocessing techniques and shows how to reconstruct certificates for them. On
the negative side, the paper discusses certain limitations of the
currently-used proof systems in the light of preprocessing. The presented
techniques were implemented and evaluated in the state-of-the-art QBF
preprocessor bloqqer.Comment: LPAR 201
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