Related papers: Proof-Stitch: Proof Combination for Divide and Con…
We introduce a new algorithm for checking satisfiability based on a calculus of Dependency sequents (D-sequents). Given a CNF formula F(X), a D-sequent is a record stating that under a partial assignment a set of variables of X is redundant…
Solving mathematical problems requires advanced reasoning abilities and presents notable challenges for large language models. Previous works usually synthesize data from proprietary models to augment existing datasets, followed by…
Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…
Constrained sampling and counting are two fundamental problems in artificial intelligence with a diverse range of applications, spanning probabilistic reasoning and planning to constrained-random verification. While the theory of these…
The SAT attack has shown to be efficient against most combinational logic encryption methods. It can be extended to attack sequential logic encryption techniques by leveraging circuit unrolling and model checking methods. However, with no…
In this paper, we present ReaS, a technique that combines numerical optimization with SAT solving to synthesize unknowns in a program that involves discrete and floating point computation. ReaS makes the program end-to-end differentiable by…
The Stabbing Planes proof system was introduced to model the reasoning carried out in practical mixed integer programming solvers. As a proof system, it is powerful enough to simulate Cutting Planes and to refute the Tseitin formulas --…
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…
Embedding-based retrieval (EBR) methods are widely used in modern recommender systems thanks to its simplicity and effectiveness. However, along the journey of deploying and iterating on EBR in production, we still identify some fundamental…
The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous…
Verification of concurrent data structures is one of the most challenging tasks in software verification. The topic has received considerable attention over the course of the last decade. Nevertheless, human-driven techniques remain…
Constraint sets can become inconsistent in different contexts. For example, during a configuration session the set of customer requirements can become inconsistent with the configuration knowledge base. Another example is the engineering…
Self-consistency (SC), a widely used decoding strategy for chain-of-thought reasoning, shows significant gains across various multi-step reasoning tasks but comes with a high cost due to multiple sampling with the preset size. Its variants,…
The $K$-armed dueling bandit problem, where the feedback is in the form of noisy pairwise comparisons, has been widely studied. Previous works have only focused on the sequential setting where the policy adapts after every comparison.…
We introduce and benchmark a stochastic local search heuristic for the NP-complete satisfiability problem 3-SAT that drastically outperforms existing solvers in the notoriously difficult realm of critically hard instances. Our construction…
Boolean Satisfiability (SAT) solvers are now routinely used in the verification of large industrial problems. However, their application in safety-critical domains such as the railways, avionics, and automotive industries requires some form…
We propose a method for exact circuit synthesis using a discrete gate set, as required for fault-tolerant quantum computing. Our approach translates the problem of synthesizing a gate specified by its unitary matrix into a boolean…
The search for increased trustworthiness of SAT solvers is very active and uses various methods. Some of these methods obtain a proof from the provers then check it, normally by replicating the search based on the proof's information.…
Instances of logical cryptanalysis, circuit verification, and bounded model checking can often be succinctly represented as a combined satisfiability (SAT) problem where an instance is a combination of traditional clauses and parity…
We study a design framework for robust, independently verifiable, and workload-balanced distributed algorithms working on a common input. An algorithm based on the framework is essentially a distributed encoding procedure for a…