Related papers: PolyAdd: Polynomial Formal Verification of Adder C…
We present verification protocols to gain confidence in the correct performance of the realization of an arbitrary universal quantum computation. The derivation of the protocols is based on the fact that matchgate computations, which are…
We consider the complexity of two questions on polynomials given by arithmetic circuits: testing whether a monomial is present and counting the number of monomials. We show that these problems are complete for subclasses of the counting…
Development of formal proofs of correctness of programs can increase actual and perceived reliability and facilitate better understanding of program specifications and their underlying assumptions. Tools supporting such development have…
An estimation method is presented for polynomial phase signals, i.e., those adopting the form of a complex exponential whose phase is polynomial in its indices. Transcending the scope of existing techniques, the proposed estimator can…
We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…
We study the problem of formal verification of Binarized Neural Networks (BNN), which have recently been proposed as a energy-efficient alternative to traditional learning networks. The verification of BNNs, using the reduction to hardware…
Verifiable learning advocates for training machine learning models amenable to efficient security verification. Prior research demonstrated that specific classes of decision tree ensembles -- called large-spread ensembles -- allow for…
Formal program verification is a longstanding goal in the field. We present the first quantitative comparison of the two primary compiler verification approaches, credible compilation/translation validation and full verification. Working…
This paper presents verification-guided development (VGD), a software engineering process we used to build Cedar, a new policy language for expressive, fast, safe, and analyzable authorization. Developing a system with VGD involves writing…
The $N$th power of a polynomial matrix of fixed size and degree can be computed by binary powering as fast as multiplying two polynomials of linear degree in~$N$. When Fast Fourier Transform (FFT) is available, the resulting complexity is…
Autonomous systems -- such as self-driving cars, autonomous drones, and automated trains -- must come with strong safety guarantees. Over the past decade, techniques based on formal methods have enjoyed some success in providing strong…
Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…
We study the problem of verification and synthesis of robust control barrier functions (CBF) for control-affine polynomial systems with bounded additive uncertainty and convex polynomial constraints on the control. We first formulate robust…
Quantum addition circuits are considered being of two types: 1) Toffolli-adder circuits which use only classical reversible gates (CNOT and Toffoli), and 2) QFT-adder circuits based on the quantum Fourier transformation. We present the…
As autonomy becomes prevalent in many applications, ranging from recommendation systems to fully autonomous vehicles, there is an increased need to provide safety guarantees for such systems. The problem is difficult, as these are large,…
Despite the vast body of research literature proposing algorithms with formal guarantees, the amount of verifiable code in today's systems remains minimal. This discrepancy stems from the inherent difficulty of verifying code, particularly…
In the digital signal processing (DSP) area, one of the most important tasks is digital filter design. Currently, this procedure is performed with the aid of computational tools, which generally assume filter coefficients represented with…
Deciding in an efficient way weak probabilistic bisimulation in the context of Probabilistic Automata is an open problem for about a decade. In this work we close this problem by proposing a procedure that checks in polynomial time the…
We consider the fundamental problem of constructing fast circuits for the carry bit computation in binary addition. Up to a small additive constant, the carry bit computation reduces to computing an \aop, i.e., a formula of type $t_0 \land…
Aiming for strong security assurance, recently there has been an increasing interest in formal verification of cryptographic constructions. This paper presents a mechanised formal verification of the popular Pedersen commitment protocol,…