Related papers: PolyAdd: Polynomial Formal Verification of Adder C…
Cloud computing platforms have created the possibility for computationally limited users to delegate demanding tasks to strong but untrusted servers. Verifiable computing algorithms help build trust in such interactions by enabling the…
Fault injection attacks represent a type of active, physical attack against cryptographic circuits. Various countermeasures have been proposed to thwart such attacks, the design and implementation of which are, however, intricate,…
A program verifier produces reliable results only if both the logic used to justify the program's correctness is sound, and the implementation of the program verifier is itself correct. Whereas it is common to formally prove soundness of…
An integer adder for integers in the binary representation is one of the basic operations of any digital processor. For adding two integers of N bits each, the serial adder takes as many clock ticks. For achieving higher speeds, parallel…
Computer algebra systems are really good at factoring polynomials, i.e. writing f as a product of irreducible factors. It is relatively easy to verify that we have a factorisation, but verifying that these factors are irreducible is a much…
Recently much attention has been paid to quantum circuit design to prepare for the future "quantum computation era." Like the conventional logic synthesis, it should be important to verify and analyze the functionalities of generated…
We establish a generic form of hardness amplification for the approximability of constant-depth Boolean circuits by polynomials. Specifically, we show that if a Boolean circuit cannot be pointwise approximated by low-degree polynomials to…
We present a deep embedding of Bellantoni and Cook's syntactic characterization of polytime functions. We prove formally that it is correct and complete with respect to the original characterization by Cobham that required a bound to be…
Software engineering of modular robotic systems is a challenging task, however, verifying that the developed components all behave as they should individually and as a whole presents its own unique set of challenges. In particular, distinct…
Decision Diagrams(DDs) are one of the most popular representations for boolean functions. They are widely used in the design and verification of circuits. Different types of DDs have been proven to represent important functions in…
We present foundational work on standard bases over rings and on Boolean Groebner bases in the framework of Boolean functions. The research was motivated by our collaboration with electrical engineers and computer scientists on problems…
We consider the task of verifying the correctness of quantum computation for a restricted class of circuits which contain at most two basis changes. This contains circuits giving rise to the second level of the Fourier Hierarchy, the lowest…
In this paper we present the formal, computer-supported verification of a functional implementation of Buchberger's critical-pair/completion algorithm for computing Gr\"obner bases in reduction rings. We describe how the algorithm can be…
Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…
Cody & Waite argument reduction technique works perfectly for reasonably large arguments but as the input grows there are no bit left to approximate the constant with enough accuracy. Under mild assumptions, we show that the result computed…
Formal Methods are mathematically-based techniques for software design and engineering, which enable the unambiguous description of and reasoning about a system's behaviour. Autonomous systems use software to make decisions without human…
New results on computing certificates of strictly positive polynomials in Archimedean quadratic modules are presented. The results build upon (i) Averkov's method for generating a strictly positive polynomial for which a membership…
Polymorphic circuits are a special kind of circuits which possess multiple build-in functions, and these functions are activated by environment parameters, like temperature, light and VDD. The behavior of a polymorphic circuit can be…
We study the safety verification problem for a class of distributed parameter systems described by partial differential equations (PDEs), i.e., the problem of checking whether the solutions of the PDE satisfy a set of constraints at a…
This paper presents a fast and effective computer algebraic method for analyzing and verifying non-linear integer arithmetic circuits using a novel algebraic spectral model. It introduces a concept of algebraic spectrum, a numerical form of…