Related papers: Sciduction: Combining Induction, Deduction, and St…
We introduce transductive program synthesis, a new formulation of the program synthesis task that explicitly leverages test inputs during synthesis. While prior approaches to program synthesis--whether based on natural language descriptions…
The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more…
The recent advancements in Deep Learning models and techniques have led to significant strides in performance across diverse tasks and modalities. However, while the overall capabilities of models show promising growth, our understanding of…
Inductive theorem proving is an important long-standing challenge in computer science. In this extended abstract, we first summarize the recent developments of proof by induction for Isabelle/HOL. Then, we propose united reasoning, a novel…
We propose a framework for synthesizing inductive invariants for incomplete verification engines, which soundly reduce logical problems in undecidable theories to decidable theories. Our framework is based on the counter-example guided…
Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence,…
Stochastic hybrid systems have received significant attentions as a relevant modelling framework describing many systems, from engineering to the life sciences: they enable the study of numerous applications, including transportation…
Current natural language systems designed for multi-step claim validation typically operate in two phases: retrieve a set of relevant premise statements using heuristics (planning), then generate novel conclusions from those statements…
Verification problems of programs written in various paradigms (such as imperative, logic, concurrent, functional, and object-oriented ones) can be reduced to problems of solving Horn clause constraints on predicate variables that represent…
AI agents increasingly excel at generating, testing, and refining code. However, they fall short on tasks requiring formal guarantees of full coverage that testing alone cannot provide. Distributed systems are a prime example: properties…
We introduce INDUCTION, a benchmark for finite structure concept synthesis in first order logic. Given small finite relational worlds with extensionally labeled target predicates, models must output a single first order logical formula that…
Infinite-state systems such as distributed protocols are challenging to verify using interactive theorem provers or automatic verification tools. Of these techniques, deductive verification is highly expressive but requires the user to…
Hybrid systems are a compact and natural mechanism with which to address problems in robotics. This work introduces an approach to learning hybrid systems from demonstrations, with an emphasis on extracting models that are explicitly…
We study induction on the program structure as a proof method for bisimulation-based compiler correctness. We consider a first-order language with mutually recursive function definitions, system calls, and an environment semantics. The…
In settings from fact-checking to question answering, we frequently want to know whether a collection of evidence (premises) entails a hypothesis. Existing methods primarily focus on the end-to-end discriminative version of this task, but…
A major bottleneck in search-based program synthesis is the exponentially growing search space which makes learning large programs intractable. Humans mitigate this problem by leveraging the compositional nature of the real world: In…
Coinduction refers to both a technique for the definition of infinite streams, so-called codata, and a technique for proving the equality of coinductively specified codata. This article first reviews coinduction in declarative programming.…
Most software verification tools can be classified into one of a number of established families, each of which has their own focus and strengths. For example, concrete counterexample generation in model checking, invariant inference in…
Program synthesis is the generation of a program from a specification. Correct synthesis is difficult, and methods that provide formal guarantees suffer from scalability issues. On the other hand, neural networks are able to generate…
Algorithms of inference in a computer system oriented to input and semantic processing of text information are presented. Such inference is necessary for logical questions when the direct comparison of objects from a question and database…