We propose a two algorithms for computation of (sharp) enclosures of definite interevals: a lor.rd adaptive dgorid~a (LAA) and a g/oba/ a&,pth~ cdgor92~n (GAA). Both algorithms are based (m Gauss-Legendre ~ladrature. Error terms are bounded using automatic differentiation in combination with interval evah:adons. Several nmnerical examples are presented; these examples include comparis~m with an...

Abstract Numerical and symbolic methods for optimization are used extensively in engineering, industry, finance. Various to reduce problems of interest ones that amenable solution by these methods. We develop a framework designing applying such reductions, using the Lean programming language interactive proof assistant. Formal verification makes process more reliable, availability an ambient ma...

Three algorithm implementations for square root computation are considered in this paper. Newton-Raphson's, iterative, and binary search algorithm implementations are completely designed, verified and compared. The algorithms, entire system-on-chip realisations and their functioning are described.

We describe GINGER, a built system for unconditional, general-purpose, and nearly practical verification of outsourced computation. GINGER is based on PEPPER, which uses the PCP theorem and cryptographic techniques to implement an efficient argument system (a kind of interactive protocol). GINGER slashes query costs via protocol refinements; broadens the computational model to include (primitiv...

We describe GINGER, a built system for unconditional, general-purpose, and nearly practical verification of outsourced computation. GINGER is based on PEPPER, which uses the PCP theorem and cryptographic techniques to implement an efficient argument system (a kind of interactive protocol). GINGER slashes the query size and costs via theoretical refinements that are of independent interest; broa...

Sturm’s Theorem is a well-known result in real algebraic geometry that provides a function that computes the number of roots of a univariate polynomial in a semiopen interval. This paper presents a formalization of this theorem in the PVS theorem prover, as well as a decision procedure that checks whether a polynomial is always positive, nonnegative, nonzero, negative, or nonpositive on any inp...

Calculational proofs—proofs by stepwise formula manipulation—are praised for their rigor, readability, and elegance. It seems desirable to reuse this style, often employed on paper, in the context of mechanized reasoning, and in particular, program verification. This work leverages the power of SMT solvers to machine-check calculational proofs at the level of detail they are usually written by ...

We describe GINGER, a built system for unconditional, general-purpose, and nearly practical verification of outsourced computation. GINGER is based on PEPPER, which uses the PCP theorem and cryptographic techniques to implement an efficient argument system (a kind of interactive protocol). GINGER slashes the query size and costs via theoretical refinements that are of independent interest; broa...