Related papers: Knowledge compilation languages as proof systems
Providing knowledge documents for large language models (LLMs) has emerged as a promising solution to update the static knowledge inherent in their parameters. However, knowledge in the document may conflict with the memory of LLMs due to…
Language-integrated query is a powerful programming construct allowing database queries and ordinary program code to interoperate seamlessly and safely. Language-integrated query techniques rely on classical results about the nested…
Pre-trained Language Models (PLMs) are trained on large amounts of unlabeled data, yet they exhibit remarkable reasoning skills. However, the trustworthiness challenges posed by these black-box models have become increasingly evident in…
The Ideal Proof System (IPS) of Grochow & Pitassi (FOCS 2014, J. ACM, 2018) is an algebraic proof system that uses algebraic circuits to refute the solvability of unsatisfiable systems of polynomial equations. One potential drawback of IPS…
The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics over systems whose branching type goes beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the…
Reachability Logic is a formalism that can be used, among others, for expressing partial-correctness properties of transition systems. In this paper we present three proof systems for this formalism, all of which are sound and complete and…
Automated reasoners, such as SAT/SMT solvers and first-order provers, are becoming the backbones of rigorous systems engineering, being used for example in applications of system verification, program synthesis, and cybersecurity.…
Multi-hop Question Answering (QA) is a challenging task since it requires an accurate aggregation of information from multiple context paragraphs and a thorough understanding of the underlying reasoning chains. Recent work in multi-hop QA…
A major difficulty in developing and maintaining very large knowledge bases originates from the variety of forms in which knowledge is made available to the KB builder. The objective of this research is to bring together two complementary…
In this work, we use large language models (LLMs) to augment and accelerate research on the P versus NP problem, one of the most important open problems in theoretical computer science and mathematics. Specifically, we propose Socratic…
Problem-solving has been a fundamental driver of human progress in numerous domains. With advancements in artificial intelligence, Large Language Models (LLMs) have emerged as powerful tools capable of tackling complex problems across…
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…
Maximum 2-satisfiability (MAX-2-SAT) is a type of combinatorial decision problem that is known to be NP-hard. In this paper, we compare LightSolver's quantum-inspired algorithm to a leading deep-learning solver for the MAX-2-SAT problem.…
Generalizations of numeration systems in which N is recognizable by a finite automaton are obtained by describing a lexicographically ordered infinite regular language L over a finite alphabet A. For these systems, we obtain a…
The computational complexity of the partition, 0-1 subset sum, unbounded subset sum, 0-1 knapsack and unbounded knapsack problems and their multiple variants were studied in numerous papers in the past where all the weights and profits were…
Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to…
We consider the problem of bottom-up compilation of knowledge bases, which is usually predicated on the existence of a polytime function for combining compilations using Boolean operators (usually called an Apply function). While such a…
We present the design, implementation, and foundation of a verifier for higher-order functional programs with generics and recursive data types. Our system supports proving safety and termination using preconditions, postconditions and…
A generalization of numeration system in which the set N of the natural numbers is recognizable by finite automata can be obtained by describing a lexicographically ordered infinite regular language. Here we show that if P belonging to Q[x]…
Some aspects of programming education are examined in this work. It is emphasised, based on the entertainment value, the most appropriate examples are chosen to demonstrate the different language constructions and data structures. Such an…