Related papers: Complete Quantum Relational Hoare Logics from Opti…
We present a variant of the quantum relational Hoare logic from (Unruh, POPL 2019) that allows us to use "expectations" in pre- and postconditions. That is, when reasoning about pairs of programs, our logic allows us to quantitatively…
Hoare logic provides a syntax-oriented method to reason about program correctness and has been proven effective in the verification of classical and probabilistic programs. Existing proposals for quantum Hoare logic either lack completeness…
Hoare logic is a foundation of axiomatic semantics of classical programs and it provides effective proof techniques for reasoning about correctness of classical programs. To offer similar techniques for quantum program verification and to…
Quantum Hoare logic (QHL) is a formal verification tool specifically designed to ensure the correctness of quantum programs. There has been an ongoing challenge to achieve a relatively complete satisfaction-based QHL with while-loop since…
Abstract interpretation, Hoare logic, and incorrectness (or reverse Hoare) logic are powerful techniques for static analysis of computer programs. All of them have been successfully extended to the quantum setting, but largely developed in…
In this paper, we present a Hoare-style logic for reasoning about quantum programs with classical variables. Our approach offers several improvements over previous work: (1) Enhanced expressivity of the programming language: Our logic…
Duality theorems play a fundamental role in convex optimization. Recently, it was shown how duality theorems for countable probability distributions and finite-dimensional quantum states can be leveraged for building relatively complete…
We present a logic for reasoning about pairs of interactive quantum programs - quantum relational Hoare logic (qRHL). This logic follows the spirit of probabilistic relational Hoare logic (Barthe et al. 2009) and allows us to formulate how…
In search for a foundational framework for reasoning about observable behavior of programs that may not terminate, we have previously devised a trace-based big-step semantics for While. In this semantics, both traces and evaluation…
In relational verification, judicious alignment of computational steps facilitates proof of relations between programs using simple relational assertions. Relational Hoare logics (RHL) provide compositional rules that embody various…
Relational Hoare logics (RHL) provide rules for reasoning about relations between programs. Several RHLs include a rule we call sequential product that infers a relational correctness judgment from judgments of ordinary Hoare logic (HL).…
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected…
In relational verification, judicious alignment of computational steps facilitates proof of relations between programs using simple relational assertions. Relational Hoare logics (RHL) provide compositional rules that embody various…
Relational Hoare logics extend the applicability of modular, deductive verification to encompass important 2-run properties including dependency requirements such as confidentiality and program relations such as equivalence or similarity…
Verifying a real-world program's functional correctness can be decomposed into (1) a refinement proof showing that the program implements a more abstract high-level program and (2) an algorithm correctness proof at the high level.…
This paper summarises the results obtained by the author and his collaborators in a program logic approach to the verification of quantum programs, including quantum Hoare logic, invariant generation and termination analysis for quantum…
A modal logic based on quantum logic is formalized in its simplest possible form. Specifically, a relational semantics and a sequent calculus are provided, and the soundness and the completeness theorems connecting both notions are…
Recently, authors have proposed under-approximate logics for reasoning about programs. So far, all such logics have been confined to reasoning about individual program behaviours. Yet there exist many over-approximate relational logics for…
Partial incorrectness logic (partial reverse Hoare logic) has recently been introduced as a new Hoare-style logic that over-approximates the weakest pre-conditions of a program and a post-condition. It is expected to verify systems where…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…