Related papers: On Backdoors To Tractable Constraint Languages
A backdoor in a finite-domain CSP instance is a set of variables where each possible instantiation moves the instance into a polynomial-time solvable class. Backdoors have found many applications in artificial intelligence and elsewhere,…
We extend the notion of a strong backdoor from the CSP setting to the Valued CSP setting (VCSP, for short). This provides a means for augmenting a class of tractable VCSP instances to instances that are outside the class but of small…
A backdoor set is a set of variables of a propositional formula such that fixing the truth values of the variables in the backdoor set moves the formula into some polynomial-time decidable class. If we know a small backdoor set we can…
Backdoor sets, a notion introduced by Williams et al. in 2003, are certain sets of key variables of a CNF formula F that make it easy to solve the formula; by assigning truth values to the variables in a backdoor set, the formula gets…
We show that CSP is fixed-parameter tractable when parameterized by the treewidth of a backdoor into any tractable CSP problem over a finite constraint language. This result combines the two prominent approaches for achieving tractability…
The Constraint Satisfaction Problem (CSP) is a central and generic computational problem which provides a common framework for many theoretical and practical applications. A central line of research is concerned with the identification of…
Answer Set Programming (ASP) is an increasingly popular framework for declarative programming that admits the description of problems by means of rules and constraints that form a disjunctive logic program. In particular, many AI problems…
There are various approaches to exploiting "hidden structure" in instances of hard combinatorial problems to allow faster algorithms than for general unstructured or random instances. For SAT and its counting version #SAT, hidden structure…
In this paper, we introduce a notion of backdoors to Reiter's propositional default logic and study structural properties of it. Also we consider the problems of backdoor detection (parameterised by the solution size) as well as backdoor…
A strong backdoor in a formula $\phi$ of propositional logic to a tractable class $\mathcal{C}$ of formulas is a set $B$ of variables of $\phi$ such that every assignment of the variables in $B$ results in a formula from $\mathcal{C}$.…
We study parameterized Constraint Satisfaction Problem for infinite constraint languages. The parameters that we study are weight of the satisfying assignment, number of constraints, maximum number of occurrences of a variable in the…
In the present paper we introduce the notion of strong backdoors into the field of temporal logic for the CNF-fragment of linear temporal logic introduced by Fisher. We study the parameterised complexity of the satisfiability problem…
Because state-of-the-art language models are expensive to train, most practitioners must make use of one of the few publicly available language models or language model APIs. This consolidation of trust increases the potency of backdoor…
Backdoor attacks pose a significant threat to Large Language Models (LLMs), where adversaries can embed hidden triggers to manipulate LLM's outputs. Most existing defense methods, primarily designed for classification tasks, are ineffective…
An instance of Max CSP is a finite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satisfied constraints. Max CSP captures many well-known problems (such as Max…
In this paper we extend the classical notion of strong and weak backdoor sets for SAT and CSP by allowing that different instantiations of the backdoor variables result in instances that belong to different base classes; the union of the…
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
In 2007 it was conjectured that the Constraint Satisfaction Problem (CSP) over a constraint language $\Gamma$ is tractable if and only if $\Gamma$ is preserved by a weak near-unanimity (WNU) operation. After many efforts and partial…
Knuth (1990) introduced the class of nested formulas and showed that their satisfiability can be decided in polynomial time. We show that, parameterized by the size of a smallest strong backdoor set to the target class of nested formulas,…