Specification synthesis with constrained Horn clauses

Prabhu, Sumanth; Fedyukovich, Grigory; Madhukar, K.; D’Souza, Deepak

doi:10.1145/3453483.3454104

Cited by 13 publications

(3 citation statements)

References 46 publications

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“…Specification engineering. The first and primary motivation stems from the observation that specification synthesis (Albarghouthi, Dillig, and Gurfinkel 2016;Prabhu et al 2021) (i.e., the process of constructing F (X, Y )) and function synthesis form part of the iterative process wherein one iteratively modifies specifications based on the functions that are constructed by the underlying engine. In this context, one helpful measure is to determine the number of possible semantically different functions that satisfy the specification, as often a large number of possible Skolem functions indicates the vagueness of specifications and highlights the need for strengthening the specification.…”

Section: Applicationsmentioning

confidence: 99%

An Approximate Skolem Function Counter

Shaw,

Juba,

Meel

2024

AAAI

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One approach to probabilistic inference involves counting the number of models of a given Boolean formula. Here, we are interested in inferences involving higher-order objects, i.e., functions. We study the following task: Given a Boolean specification between a set of inputs and outputs, count the number of functions of inputs such that the specification is met. Such functions are called Skolem functions. We are motivated by the recent development of scalable approaches to Boolean function synthesis. This stands in relation to our problem analogously to the relationship between Boolean satisfiability and the model counting problem. Yet, counting Skolem functions poses considerable new challenges. From the complexity-theoretic standpoint, counting Skolem functions is not only #P-hard; it is quite unlikely to have an FPRAS (Fully Polynomial Randomized Approximation Scheme) as the problem of synthesizing a Skolem function remains challenging, even given access to an NP oracle. The primary contribution of this work is the first algorithm, SkolemFC, that computes the number of Skolem functions. SkolemFC relies on technical connections between counting functions and propositional model counting: our algorithm makes a linear number of calls to an approximate model counter and computes an estimate of the number of Skolem functions with theoretical guarantees. Our prototype displays impressive scalability, handling benchmarks comparably to state-of-the-art Skolem function synthesis engines, even though counting all such functions ostensibly poses a greater challenge than synthesizing a single function.

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Section: Applicationsmentioning

confidence: 99%

An Approximate Skolem Function Counter

Shaw,

Juba,

Meel

2024

AAAI

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“…Given that the subtyping constraints can be expressed in the form of constrained Horn clauses (CHC) and not all the subtyping constraints need to hold, the problem above is essentially a CHC solving problem with weak constraints and maximality [22] where the optimization objective of the problem is defined by pointwise logical comparison of the solutions.…”

Section: Overview Of Type Inference and Checking In Gratenmentioning

confidence: 99%

Gradual Tensor Shape Checking

Hattori

Kobayashi

Satô

2023

Lecture Notes in Computer Science

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Tensor shape mismatch is a common source of bugs in deep learning programs. We propose a new type-based approach to detect tensor shape mismatches. One of the main features of our approach is the best-effort shape inference. As the tensor shape inference problem is undecidable in general, we allow static type/shape inference to be performed only in a best-effort manner. If the static inference cannot guarantee the absence of the shape inconsistencies, dynamic checks are inserted into the program. Another main feature is gradual typing, where users can improve the precision of the inference by adding appropriate type annotations to the program. We formalize our approach and prove that it satisfies the criteria of gradual typing proposed by Siek et al. in 2015. We have implemented a prototype shape checking tool based on our approach and evaluated its effectiveness by applying it to some deep neural network programs.

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“…We motivate our work from the domain of open programs [29,32] using Figure 1. The data types nat and list-corresponding to the term algebras of natural numbers and lists in first-order logic-are defined inductively using constructors as given by the first-order formulas (nat.1)-(list.3).…”

Section: Motivating Examplementioning

confidence: 99%

Rewriting and Inductive Reasoning

Hajdu,

Kovács,

Rawson

EPiC Series in Computing

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Rewriting techniques based on reduction orderings generate “just enough” consequences to retain first-order completeness. This is ideal for superposition-based first-order theorem proving, but for at least one approach to inductive reasoning we show that we are miss- ing crucial consequences. We therefore extend the superposition calculus with rewriting- based techniques to generate sufficient consequences for automating induction in satura- tion. When applying our work within the unit-equational fragment, our experiments with the theorem prover Vampire show significant improvements for inductive reasoning.

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Specification synthesis with constrained Horn clauses

Cited by 13 publications

References 46 publications

An Approximate Skolem Function Counter

An Approximate Skolem Function Counter

Gradual Tensor Shape Checking

Rewriting and Inductive Reasoning

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