13 research outputs found
Beyond Hypertree Width: Decomposition Methods Without Decompositions
The general intractability of the constraint satisfaction problem has
motivated the study of restrictions on this problem that permit polynomial-time
solvability. One major line of work has focused on structural restrictions,
which arise from restricting the interaction among constraint scopes. In this
paper, we engage in a mathematical investigation of generalized hypertree
width, a structural measure that has up to recently eluded study. We obtain a
number of computational results, including a simple proof of the tractability
of CSP instances having bounded generalized hypertree width
On Tackling the Limits of Resolution in SAT Solving
The practical success of Boolean Satisfiability (SAT) solvers stems from the
CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a
propositional proof complexity perspective, CDCL is no more powerful than the
resolution proof system, for which many hard examples exist. This paper
proposes a new problem transformation, which enables reducing the decision
problem for formulas in conjunctive normal form (CNF) to the problem of solving
maximum satisfiability over Horn formulas. Given the new transformation, the
paper proves a polynomial bound on the number of MaxSAT resolution steps for
pigeonhole formulas. This result is in clear contrast with earlier results on
the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper
also establishes the same polynomial bound in the case of modern core-guided
MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard
for CDCL SAT solvers, show that these can be efficiently solved with modern
MaxSAT solvers
Beyond Q-Resolution and Prenex Form: A Proof System for Quantified Constraint Satisfaction
We consider the quantified constraint satisfaction problem (QCSP) which is to
decide, given a structure and a first-order sentence (not assumed here to be in
prenex form) built from conjunction and quantification, whether or not the
sentence is true on the structure. We present a proof system for certifying the
falsity of QCSP instances and develop its basic theory; for instance, we
provide an algorithmic interpretation of its behavior. Our proof system places
the established Q-resolution proof system in a broader context, and also allows
us to derive QCSP tractability results
On the Relative Strength of Pebbling and Resolution
The last decade has seen a revival of interest in pebble games in the context
of proof complexity. Pebbling has proven a useful tool for studying
resolution-based proof systems when comparing the strength of different
subsystems, showing bounds on proof space, and establishing size-space
trade-offs. The typical approach has been to encode the pebble game played on a
graph as a CNF formula and then argue that proofs of this formula must inherit
(various aspects of) the pebbling properties of the underlying graph.
Unfortunately, the reductions used here are not tight. To simulate resolution
proofs by pebblings, the full strength of nondeterministic black-white pebbling
is needed, whereas resolution is only known to be able to simulate
deterministic black pebbling. To obtain strong results, one therefore needs to
find specific graph families which either have essentially the same properties
for black and black-white pebbling (not at all true in general) or which admit
simulations of black-white pebblings in resolution. This paper contributes to
both these approaches. First, we design a restricted form of black-white
pebbling that can be simulated in resolution and show that there are graph
families for which such restricted pebblings can be asymptotically better than
black pebblings. This proves that, perhaps somewhat unexpectedly, resolution
can strictly beat black-only pebbling, and in particular that the space lower
bounds on pebbling formulas in [Ben-Sasson and Nordstrom 2008] are tight.
Second, we present a versatile parametrized graph family with essentially the
same properties for black and black-white pebbling, which gives sharp
simultaneous trade-offs for black and black-white pebbling for various
parameter settings. Both of our contributions have been instrumental in
obtaining the time-space trade-off results for resolution-based proof systems
in [Ben-Sasson and Nordstrom 2009].Comment: Full-length version of paper to appear in Proceedings of the 25th
Annual IEEE Conference on Computational Complexity (CCC '10), June 201
On the speed of constraint propagation and the time complexity of arc consistency testing
Establishing arc consistency on two relational structures is one of the most
popular heuristics for the constraint satisfaction problem. We aim at
determining the time complexity of arc consistency testing. The input
structures and can be supposed to be connected colored graphs, as the
general problem reduces to this particular case. We first observe the upper
bound , which implies the bound in terms of
the number of edges and the bound in terms of the number of
vertices. We then show that both bounds are tight up to a constant factor as
long as an arc consistency algorithm is based on constraint propagation (like
any algorithm currently known).
Our argument for the lower bounds is based on examples of slow constraint
propagation. We measure the speed of constraint propagation observed on a pair
by the size of a proof, in a natural combinatorial proof system, that
Spoiler wins the existential 2-pebble game on . The proof size is bounded
from below by the game length , and a crucial ingredient of our
analysis is the existence of with . We find one
such example among old benchmark instances for the arc consistency problem and
also suggest a new, different construction.Comment: 19 pages, 5 figure
How to Deal with Unbelievable Assertions
We tackle the problem that arises when an agent receives unbelievable information. Information is unbelievable if it conflicts with the agent’s convictions, that is, what the agent considers knowledge. We propose two solutions based on modifying the information so that it is no longer unbelievable. In one solution, the source and the receiver of the information cooperatively resolve the conflict. For this purpose we introduce a dialogue protocol in which the receiver explains what is wrong with the information by using logical interpolation, and the source produces a new assertion accordingly. If such cooperation is not possible, we propose an alternative solution in which the receiver revises the new piece of information by its own convictions to make it acceptable.Peer reviewe
Formal verification: further complexity issues and applications
Prof. Giacomo Cioffi (Università di Roma "La Sapienza"), Prof. Fabio Panzieri (Università di Bologna), Dott.ssa Carla Limongelli (Università di Roma Tre)