Probabilistic Generalization of Backdoor Trees with Application to SAT
نویسندگان
چکیده
The concept of Strong Backdoor Sets (SBS) for Constraint Satisfaction Problems is well known as one the attempts to exploit structural peculiarities in hard instances. However, practice, finding an SBS a particular instance often harder than solving it. Recently, probabilistic weakened variant was introduced: SBS, all subproblems must be polynomially solvable, whereas only large fraction ρ them should have this property. This new backdoors called ρ-backdoors makes it possible use Monte Carlo method and metaheuristic optimization find with very close 1, relatively fast. Despite fact that ρ-backdoor-based decomposition portion remain, practice narrowing search space allows problem faster such backdoor without In paper, we significantly improve on by extending trees: introduce ρ-backdoor trees, show interconnections between ρ-backdoors, corresponding establish some theoretical properties trees. experimental part moving from trees drastically reducing time required construct decompositions compromising their quality.
منابع مشابه
Backdoor Treewidth for SAT
A strong backdoor in a CNF formula is a set of variables such that each possible instantiation of these variables moves the formula into a tractable class. The algorithmic problem of finding a strong backdoor has been the subject of intensive study, mostly within the parameterized complexity framework. Results to date focused primarily on backdoors of small size. In this paper we propose a new ...
متن کاملBackdoor Trees
The surprisingly good performance of modern satisfiability (SAT) solvers is usually explained by the existence of a certain “hidden structure” in real-world instances. We introduce the notion of backdoor trees as an indicator for the presence of a hidden structure. Backdoor trees refine the notion of strong backdoor sets, taking into account the relationship between backdoor variables. We prese...
متن کاملBackdoor Trees for Answer Set Programming
We translate the concept of backdoor trees from SAT to propositional Answer Set Programming (ASP). By means of backdoor trees we can reduce a reasoning task for a general ASP instance to reasoning tasks on several tractable ASP instances. We demonstrate that the number of tractable ASP instances can be drastically reduced in comparison to a related approach based on strong backdoors.
متن کاملSound Probabilistic #SAT with Projection
The #SAT problem is concerned with counting the number of models of a boolean formula. Since #SAT is a computationally difficult problem, not only exact but also approximative solutions are of interest. A powerful approximation method is probabilistic approximation, making use of random sampling. We call a probabilistic approximation method sound when the probability and magnitude of the sampli...
متن کاملA Generalization of SAT and #SAT for Robust Policy Evaluation
Both SAT and #SAT can represent difficult problems in seemingly dissimilar areas such as planning, verification, and probabilistic inference. Here, we examine an expressive new language, #∃SAT, that generalizes both of these languages. #∃SAT problems require counting the number of satisfiable formulas in a concisely-describable set of existentially-quantified, propositional formulas. We charact...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the ... AAAI Conference on Artificial Intelligence
سال: 2023
ISSN: ['2159-5399', '2374-3468']
DOI: https://doi.org/10.1609/aaai.v37i4.25525