Zhaowei Xu

LABORATOIRE MÉTHODES FORMELLES · Université de Paris-Saclay

Hoare logic for the set of while-programs with the first-order logical language L and the first-order theory T⊂L is denoted by HL(T). Bergstra and Tucker have pointed out that the complete number theory Th(N) is the only extension T of Peano arithmetic PA for which HL(T) is logically complete. The completeness result is not satisfying, since it all...

In this paper, we introduce dynamic lifting to a quantum circuit-description language, following the Proto-Quipper language approach. Dynamic lifting allows programs to transfer the result of measuring quantum data -- qubits -- into classical data -- booleans -- . We propose a type system and an operational semantics for the language and we state s...

While recent progress in quantum hardware open the door for significant speedup in certain key areas (cryptography, biology, chemistry, optimization, machine learning, etc), quantum algorithms are still hard to implement right, and the validation of such quantum programs is achallenge. Moreover, importing the testing and debugging practices at use...

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 that recursion will become one of the fundamental paradigms of quantum programming. Several program logics have...

In this paper, we propose compositional separation logic with tree predicates (CSLTP), where properties such as sortedness and height-balancedness of complex data structures (for instance, AVL trees and red-black trees) can be fully specified. We show that the satisfiability problem of CSLTP is decidable. The main technical ingredient of the decisi...

ACTL formulas with linear counterexamples have been studied and the templates of ACTL formulas for which linear counterexamples exist have been identified. This paper further studies ACTL formulas having linear counterexamples in light of bounded semantics, and an application of this to SAT-based verification (in particular, bounded correctness che...

The nonstandard approach to program semantics has successfully resolved the completeness problem of Floyd-Hoare logic. The known versions of nonstandard semantics, the Hungary semantics and axiomatic semantics, are so general that they are absent either from mathematical elegance or from practical usefulness. The aim of this paper is to exhibit a n...

The general completeness problem of Hoare logic relative to the standard model $N$ of Peano arithmetic has been studied by Cook, and it allows for the use of arbitrary arithmetical formulas as assertions. In practice, the assertions would be simple arithmetical formulas, e.g. of a low level in the arithmetical hierarchy. In addition, we find that,...

The general completeness problem of Hoare logic relative to the standard model N of Peano arithmetic has been studied by Cook, and it allows for the use of arbitrary arithmetical formulas as assertions. In practice, the assertions would be simple arithmetical formulas, e.g. of a low level in the arithmetical hierarchy. This paper further studies th...

Hoare's logic is an axiomatic system of proving programs correct, which has been extended to be a separation logic to reason about mutable heap structure. We develop the most fundamental logical structure of strongest postcondition of Hoare's logic in Peano's arithmetic $PA$. Let $p\in L$ and $S$ be any while-program. The arithmetical definability...