Related papers: Reasoning about Recursive Quantum Programs
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
Quantum algorithms for tasks such as factorization, search, and simulation rely on control flow such as branching and iteration that depends on the value of data in superposition. High-level programming abstractions for control flow, such…
We present an expressive logic over trace formulas, based on binary state predicates, chop, and least fixed-points, for precise specification of programs with recursive procedures. Both, programs and trace formulas, are equipped with a…
Designing scalable concurrent objects, which can be efficiently used on multicore processors, often requires one to abandon standard specification techniques, such as linearizability, in favor of more relaxed consistency requirements.…
This study considers implementations of error correction in a simulation language on a classical computer. Error correction will be necessarily in quantum computing and quantum information. We will give some examples of the implementations…
Recent trends in AI verification and Explainable AI have raised the question of whether AI planning techniques can be verified. In this paper, we present a novel resource logic, the Proof Carrying Plans (PCP) logic that can be used to…
A recent experiment testing the necessity of complex numbers in the standard formulation of quantum theory is recreated using IBM quantum computers. To motivate the experiment, we present a basic construction for real-valued quantum theory.…
One recurring problem in program development is that of understanding how to re-use code developed by a third party. In the context of (constraint) logic programming, part of this problem reduces to figuring out how to query a program. If…
Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable…
How should future neural reasoning systems implement extended computation? Recursive Reasoning Models (RRMs) offer a promising alternative to autoregressive sequence extension by performing iterative latent-state refinement with shared…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
We propose a simple imperative programming language, ERC, that features arbitrary real numbers as primitive data type, exactly. Equipped with a denotational semantics, ERC provides a formal programming language-theoretic foundation to the…
Case-Based Reasoning (CBR) is an artificial intelligence approach to problem-solving with a good record of success. This article proposes using Quantum Computing to improve some of the key processes of CBR, such that a Quantum Case-Based…
Weak memory models specify the semantics of concurrent programs on multi-core architectures. Reasoning techniques for weak memory models are often specialized to one fixed model and verification results are hence not transferable to other…
A proof of quantumness is an efficiently verifiable interactive test that an efficient quantum computer can pass, but all efficient classical computers cannot (under some cryptographic assumption). Such protocols play a crucial role in the…
Some total languages, like Agda and Coq, allow the use of guarded corecursion to construct infinite values and proofs. Guarded corecursion is a form of recursion in which arbitrary recursive calls are allowed, as long as they are guarded by…
We propose and implement a family of quantum-informed recursive optimization (QIRO) algorithms for combinatorial optimization problems. Our approach leverages quantum resources to obtain information that is used in problem-specific…
Rely-guarantee (RG) logic uses thread interference specifications (relies and guarantees) to reason about the correctness of multithreaded software. Unfortunately, RG logic requires each function postcondition to be "stabilized" or…
Current quantum processors are noisy, have limited coherence and imperfect gate implementations. On such hardware, only algorithms that are shorter than the overall coherence time can be implemented and executed successfully. A good quantum…