arXiv subjects

Sorin Stratulat

Publications and source records attributed to Sorin Stratulat.

4 recordsLinked to original sources

arXiv2026

Certification of Bilateral Patience Sort in Theorema and Rocq

This is a case study on a specific version of the Patience Sort algorithm in which we illustrate the evolution of it from an intuitive but inefficient nested recursion into a more complex but more efficient tail recursion, together with its formal implementation and certification in Theorema and Rocq (formerly Coq). We identify some general principles of algorithm transformation, and we develop the necessary background theory and proof methods. As a significant distinctive aspect, the approach in Theorema uses multisets, which simplifies the whole process and makes it more intuitive. The certification process reveals significant differences between the Theorema and Rocq approaches, about which we provide a comparative analysis with respect to algorithm definition, proof development, and proof effort. This analysis offers insights into how algorithm design influences the complexity and structure of formal proofs and demonstrates how non-trivial algorithms can be effectively verified across different formal frameworks.

cs.LO↗

arXiv2021

E-Cyclist: Implementation of an Efficient Validation of FOLID Cyclic Induction Reasoning

Checking the soundness of cyclic induction reasoning for first-order logic with inductive definitions (FOLID) is decidable but the standard checking method is based on an exponential complement operation for Büchi automata. Recently, we introduced a polynomial checking method whose most expensive steps recall the comparisons done with multiset path orderings. We describe the implementation of our method in the Cyclist prover. Referred to as E-Cyclist, it successfully checked all the proofs included in the original distribution of Cyclist. Heuristics have been devised to automatically define, from the analysis of the proof derivations, the trace-based ordering measures that guarantee the soundness property.

cs.LO↗

arXiv2018

Validating Back-links of FOLID Cyclic Pre-proofs

Cyclic pre-proofs can be represented as sets of finite tree derivations with back-links. In the frame of the first-order logic with inductive definitions, the nodes of the tree derivations are labelled by sequents and the back-links connect particular terminal nodes, referred to as buds, to other nodes labelled by a same sequent. However, only some back-links can constitute sound pre-proofs. Previously, it has been shown that special ordering and derivability conditions, defined along the minimal cycles of the digraph representing a particular normal form of the cyclic pre-proof, are sufficient for validating the back-links. In that approach, a same constraint could be checked several times when processing different minimal cycles, hence one may require additional recording mechanisms to avoid redundant computation in order to downgrade the time complexity to polynomial. We present a new approach that does not need to process minimal cycles. It based on a normal form that allows to define the validation conditions by taking into account only the root-bud paths from the non-singleton strongly connected components of its digraph.

cs.LO↗

arXiv2013

Performing Implicit Induction Reasoning with Certifying Proof Environments

Largely adopted by proof assistants, the conventional induction methods based on explicit induction schemas are non-reductive and local, at schema level. On the other hand, the implicit induction methods used by automated theorem provers allow for lazy and mutual induction reasoning. In this paper, we present a new tactic for the Coq proof assistant able to perform automatically implicit induction reasoning. By using an automatic black-box approach, conjectures intended to be manually proved by the certifying proof environment that integrates Coq are proved instead by the Spike implicit induction theorem prover. The resulting proofs are translated afterwards into certified Coq scripts.

cs.LO↗