Related papers: Recursive Backdoors for SAT
Let $K$ be an algebraically closed field of arbitrary characteristic, $X$ an irreducible variety and $Y$ an irreducible projective variety over $K$, both are not necessarily smooth. Let $f:X\rightarrow X$ and $g:Y\rightarrow Y$ be dominant…
We present a recursive formulation of the Horn algorithm for deciding the satisfiability of propositional clauses. The usual presentations in imperative pseudo-code are informal and not suitable for simple proofs of its main properties. By…
In many decision-making processes, one may prefer multiple solutions to a single solution, which allows us to choose an appropriate solution from the set of promising solutions that are found by algorithms. Given this, finding a set of…
Usual math sets have special types: countable, compact, open, occasionally Borel, rarely projective, etc. Each such set is described by a single Set Theory formula with parameters unrelated to other formulas. Exotic expressions involving…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
Smooth backfitting has proven to have a number of theoretical and practical advantages in structured regression. Smooth backfitting projects the data down onto the structured space of interest providing a direct link between data and…
In this short paper we present a survey of some results concerning the random SAT problems. To elaborate, the Boolean Satisfiability (SAT) Problem refers to the problem of determining whether a given set of $m$ Boolean constraints over $n$…
Backdoor mechanisms have traditionally been studied as security threats that compromise the integrity of machine learning models. However, the same mechanism -- the conditional activation of specific behaviors through input triggers -- can…
The deployment of Large Reasoning Models (LRMs) in high-stakes decision-making pipelines has introduced a novel and opaque attack surface: reasoning backdoors. In these attacks, the model's intermediate Chain-of-Thought (CoT) is manipulated…
Recent studies revealed that deep learning is susceptible to backdoor poisoning attacks. An adversary can embed a hidden backdoor into a model to manipulate its predictions by only modifying a few training data, without controlling the…
It is well known that different solution strategies work well for different types of instances of hard combinatorial problems. As a consequence, most solvers for the propositional satisfiability problem (SAT) expose parameters that allow…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
Pearl's Causal Hierarchy (PCH) is a central framework for reasoning about probabilistic, interventional, and counterfactual statements, yet the satisfiability problem for PCH formulas is computationally intractable in almost all classical…
We propose a polynomially bounded, in time and space, method to decide whether a given 3-SAT formula is satisfiable or not. The tools we use here are, in fact, very simple. We first decide satisfiability for a particular 3-SAT formula,…
Inspired by Leivant's work on absolute predicativism, Bellantoni and Cook in 1992 introduced a structurally restricted form of recursion called predicative recursion. Using this recursion scheme on the inductive structures of natural…
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…
We provide a parameterized polynomial algorithm for the propositional model counting problem #SAT, the runtime of which is single-exponential in the rank-width of a formula. Previously, analogous algorithms have been known -- e.g.~[Fischer,…
In this paper we propose the approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance…
Backdoor attack intends to embed hidden backdoor into deep neural networks (DNNs), so that the attacked models perform well on benign samples, whereas their predictions will be maliciously changed if the hidden backdoor is activated by…
A backdoor attack in deep learning inserts a hidden backdoor in the model to trigger malicious behavior upon specific input patterns. Existing detection approaches assume a metric space (for either the original inputs or their latent…