arXiv subjects

Arnold Beckmann

Publications and source records attributed to Arnold Beckmann.

5 recordsLinked to original sources

arXiv2025

Access Hoare Logic

Following Hoare's seminal invention, now called Hoare logic, to reason about correctness of computer programs, we advocate a related but fundamentally different approach to reason about access security of computer programs such as access control. We define the formalism, which we denote access Hoare logic, and present examples which demonstrate its usefulness and fundamental difference to Hoare logic. We prove soundness and completeness of access Hoare logic, and provide a link between access Hoare logic and standard Hoare logic. We also demonstrate a fundamental difference of access Hoare logic to other approaches, in particular incorrectness logic.

cs.LO↗

arXiv2022

On proving consistency of equational theories in Bounded Arithmetic

We consider pure equational theories that allow substitution but disallow induction, which we denote as PETS, based on recursive definition of their function symbols. We show that the Bounded Arithmetic theory $S^1_2$ proves the consistency of PETS. Our approach employs models for PETS based on approximate values resembling notions from domain theory in Bounded Arithmetic, which may be of independent interest.

math.LO↗

arXiv2022

Verification of Bitcoin Script in Agda using Weakest Preconditions for Access Control

This paper contributes to the verification of programs written in Bitcoin's smart contract language SCRIPT in the interactive theorem prover Agda. It focuses on the security property of access control for SCRIPT programs that govern the distribution of Bitcoins. It advocates that weakest preconditions in the context of Hoare triples are the appropriate notion for verifying access control. It aims at obtaining human-readable descriptions of weakest preconditions in order to close the validation gap between user requirements and formal specification of smart contracts. As examples for the proposed approach, the paper focuses on two standard SCRIPT programs that govern the distribution of Bitcoins, Pay to Public Key Hash (P2PKH) and Pay to Multisig (P2MS). The paper introduces an operational semantics of the SCRIPT commands used in P2PKH and P2MS, which is formalised in the Agda proof assistant and reasoned about using Hoare triples. Two methodologies for obtaining human-readable descriptions of weakest preconditions are discussed: (1) a step-by-step approach, which works backwards instruction by instruction through a script, sometimes grouping several instructions together; (2) symbolic execution of the code and translation into a nested case distinction, which allows to read off weakest preconditions as the disjunction of conjunctions of conditions along accepting paths. A syntax for equational reasoning with Hoare Triples is defined in order to formalise those approaches in Agda. Keywords and phrases: Blockchain; Cryptocurrency; Bitcoin; Agda; Verification; Hoare logic; Bitcoin script; P2PKH; P2MS; Access control; Weakest precondition; Predicate transformer semantics; Provable correctness; Symbolic execution; Smart contracts

cs.SC↗

arXiv2007

On the computational complexity of cut-reduction

Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all the known results on definable functions of certain such theories can be reobtained in a uniform way.

cs.LO↗

arXiv2004

Continuous Fraisse Conjecture

We investigate the relation of countable closed subsets of the reals with respect to continuous monotone embeddability; we show that there are exactly aleph_1 many equivalence classes with respect to this embeddability relation. This is an extension of Laver's 1971 result, who considered (plain) embeddability, which yields coarser equivalence classes. Using this result we show that there are only countably many different Godel logics.

math.LO↗