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About 1,287 papers for “algorithm correctness proof”

Peterson’s algorithm Total correctness proof in IPCL

Zhygallo, A.A. · Open Publication Harvester of National Academy of Sciences of Ukraine · 2018

The total correctness of the Peterson’s Algorithm has been proved. States and transitions were fixed by the program. Runtime environment considered is interleaving concurrency with shared memory. Invariant of the program was constructed. All reasoning provided in terms of Method for software properties proof in Interleaving Parallel Compositional Languages (IPCL). Conclusions about adequacy of the Method usage for such a kind of tasks (thanks to flexibility of composition-nominative platform) and its practicality as well as ease of use for real-world systems have been made based on this and other author’s works.Problems in programming 2016; 2-3: 113-118

Cited by 0

Peterson’s algorithm Total correctness proof in IPCL

A.A. Zhygallo · PROBLEMS IN PROGRAMMING · 2016

The total correctness of the Peterson’s Algorithm has been proved. States and transitions were fixed by the program. Runtime environment considered is interleaving concurrency with shared memory. Invariant of the program was constructed. All reasoning provided in terms of Method for software properties proof in Interleaving Parallel Compositional Languages (IPCL). Conclusions about adequacy of the Method usage for such a kind of tasks (thanks to flexibility of composition-nominative platform) and its practicality as well as ease of use for real-world systems have been made based on this and other author’s works.

Cited by 0Open access

Automatic proof of correctness of a binary addition algorithm

J Strother Moore · ACM SIGART Bulletin · 1975

The Boyer-Moore Pure LISP Theorem Prover ([1], [2], and [3]) has recently proved the correctness of a program implementing binary addition with a carry flag. Because of the relative complexity of the binary addition algorithm and the automatic nature of the proof, this result was thought interesting enough to warrant this technical note.

Cited by 5

A Formal Correctness Proof of Edmonds’ Blossom Shrinking Algorithm

Mohammad Abdulaziz, Kurt Mehlhorn · Journal of Automated Reasoning · 2026

Abstract We present the first formal correctness proof of Edmonds’ blossom shrinking algorithm for maximum cardinality matching in general graphs. We focus on formalising the mathematical structures and properties that allow the algorithm to run in worst-case polynomial running time. We formalise Berge’s lemma, blossoms and their properties, and a mathematical model of the algorithm, showing that it is totally correct. We provide the first detailed proofs of many of the facts underlying the algorithm’s correctness.

Cited by 0Open access

Automated Correctness Proof of Algorithm Variants in Elliptic Curve Cryptography

Maxim Anikeev, Felix Madlener, Andreas Schlösser et al. · SHILAP Revista de lepidopterología · 2010

The Elliptic Curve Cryptography (ECC) is widely known as secure and reliable cryptographic scheme. In many situations the original cryptographic algorithm is modified to improve its efficiency in terms like power consumption or memory consumption which were not in the focus of the original algorithm. For all this modification it is crucial that the functionality and correctness of the original algorithm is preserved. In particular, various projective coordinate systems are applied in order to reduce the computational complexity of elliptic curve encryption by avoiding division in finite fields. This work investigates the possibilities of automated proofs on the correctness of different algorithmic variants. We introduce the theorems which are required to prove the correctness of a modified algorithm variant and the lemmas and definitions which are necessary to prove these goals. The correctness proof of the projective coordinate system transformation has practically been performed with the help of the an interactive formal verification system XeriFun.

Cited by 1Open access

A Proof Method based on Folding Lemmas: Applications to Algorithm Correctness

Laurent Fribourg, Staffan Bonnier, Staffan Bonnier · 2007

In [Fri92] a proof method was developed for proving arithmetic consequences of Horn clause programs defined over integer lists and integers. To be applicable, the method requires the recursion schemes of all predicates involved to be compatible. This is to guarantee a sequence of unfold transformations to eventually lead to a foldable clause. In this paper we consider the case when such a compatibility is not present. To enable folding folding lemmas are constructed. The proof then proceeds using the old method, and the theorem is proved with the lemmas as hypotheses. The method is illustrated by proving correctness criteria for Boyer and Moore's string matching algorithm and for Dijkstra's descending subsequence algorithm. 1 Introduction In [Fri92], a method was developed for proving implications of the form: p 1 (L; X 1 ) : : : p n (L; X n ) =) a(X 1 : : : X n ) where L is a list variable, each X i is a vector of integer variables, and a(X 1 : : : X n ) is an arithmetic formula. ...

Cited by 0

Correctness Proof of Ben-Or's Randomized Consensus Algorithm

Marcos Kawazoe, Aguilera Sam Toueg · 1998

We present a correctness proof for Ben-Or's Randomized Consensus Algorithm for the case in which processes can fail by crashing, and a majority of processes is correct. This is the rst time that the proof of Ben-Or's algorithm appears for this case. The proof has been extracted from [AT96]: it is a simplication of the correctness proof of a more complex consensus algorithm that involves both randomization and failure detection. 1

Cited by 0

A Correctness Proof for a Practical Byzantine-Fault-Tolerant Replication Algorithm

Miguel Castro, Barbara Liskov · DSpace@MIT (Massachusetts Institute of Technology) · 1999

This paper presents a formal specification for the unoptimized version of our algorithm presented in Section 4 of [4] and proves its safety (but not its liveness.) The specification uses the I/O automaton formalism of Tuttle an Lynch [8] and the proof is based on invariant assertions and simulation relations

Cited by 67Open access