In this work we give an alterative proof of one of basic properties of zonal polynomials and generalised it for Jack polynomials

ion-Carrying Code Elvira Albert, Germán Puebla, and Manuel Hermenegildo 1 DSIP, Universidad Complutense Madrid 2 Facultad de Informática, Technical University of Madrid 3 Depts. of Comp. Sci. and El. and Comp. Eng., U. of New Mexico Abstract. Proof-Carrying Code (PCC) is a general approach to mobile code safety in which programs are augmented with a certificate (or proof). The practical uptake ...

We define the notion of formal proof sketch for the mathematical language Mizar. We show by examples that formal proof sketches are very close to informal mathematical proofs. We discuss some ways in which formal proof sketches might be used to improve mathematical proof assistants.

: 1, if n = 1, 0, if p|n for some prime p, (−1), if n = p1p2 · · · pr, where pi are distinct primes. as e.g., its multiplicativity. To enable smooth reasoning about the sum of this number-theoretic function, we introduced an underlying many-sorted set indexed by the set of natural numbers. Its elements are just values of the Möbius function. The second part of the paper is devoted to the notion...

Raziel combines secure multi-party computation and proof-carrying code to provide privacy, correctness and verifiability guarantees for smart contracts on blockchains. Effectively solving DAO and Gyges attacks, this paper describes an implementation and presents examples to demonstrate its practical viability (e.g., private and verifiable crowdfundings and investment funds, double auctions for ...

In this article, we first briefly present a proof assistant called the Predicate Prover, which essentially offers two functionalities: (1) an automatic semi-decision procedure for First Order Predicate Calculus, and (2) a systematic translation of statements written within Set Theory into equivalent ones in First Order Predicate Calculus. We then show that the automatic usage of this proof assi...

We present a scalable, practical Hoare Logic and refinement calculus for the nondeterministic state monad with exceptions and failure in Isabelle/HOL. The emphasis of this formalisation is on large-scale verification of imperative-style functional programs, rather than expressing monad calculi in full generality. We achieve scalability in two dimensions. The method scales to multiple team membe...

A general game player is a system that understands the rules of unknown games and learns to play these games well without human intervention. A major challenge for research in General Game Playing is to endow a player with the ability to extract and prove game-specific knowledge from the mere game rules. We define a formal language to express temporally extended—yet local—properties of games. W...

In developing these techniques, temporal proof is often required, and we base our work on practical proof techniques for the clausal resolution method for propositional linear-time temporal logic PLTL. The method is based on an intuitive clausal form, called SNF, comprising three main clause types and a small number of resolution rules [11, 14]. While the approach has been shown to be competiti...