Related papers: Verifying Sampling Algorithms via Distributional I…
This paper introduces a new algorithm for the fundamental problem of generating a random integer from a discrete probability distribution using a source of independent and unbiased random coin flips. We prove that this algorithm, which we…
We lay out novel foundations for the computer-aided verification of guaranteed bounds on expected outcomes of imperative probabilistic programs featuring (i) general loops, (ii) continuous distributions, and (iii) conditioning. To handle…
A particularly challenging problem in AI safety is providing guarantees on the behavior of high-dimensional autonomous systems. Verification approaches centered around reachability analysis fail to scale, and purely statistical approaches…
Many foundational program verification tools have been developed to build machine-checked program correctness proofs, a majority of which are based on Hoare logic. Their program logics, their assertion languages, and their underlying…
We consider the problem of how to verify the security of probabilistic oblivious algorithms formally and systematically. Unfortunately, prior program logics fail to support a number of complexities that feature in the semantics and…
Loop invariants play a central role in the verification of imperative programs. However, finding these invariants is often a difficult and time-consuming task for the programmer. We have previously shown how program transformation can be…
This paper proposes a model validation method that incorporates error due to numerical procedures. Two identified models for Sine Map and Duffing-Ueda Circuit systems have been investigated. The indexes RMSE and MAPE have been applied. We…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
Probabilistic programming languages (PPLs) are expressive means for creating and reasoning about probabilistic models. Unfortunately hybrid probabilistic programs, involving both continuous and discrete structures, are not well supported by…
Hoare-style verification provides a principled foundation for reasoning about the correctness of quantum programs, but existing approaches do not allow fully automatic verification. While automata-based verification scales well when…
Programs using random values can either make all choices in advance (eagerly) or sample as needed (lazily). In formal proofs, we focus on indistinguishability between two lazy programs, a common requirement in the random oracle model (ROM).…
We introduce an automata-theoretic method for the verification of distributed algorithms running on ring networks. In a distributed algorithm, an arbitrary number of processes cooperate to achieve a common goal (e.g., elect a leader).…
1) We introduce random discrete Morse theory as a computational scheme to measure the complicatedness of a triangulation. The idea is to try to quantify the frequence of discrete Morse matchings with a certain number of critical cells. Our…
Assessing the validity of a real-world system with respect to given quality criteria is a common yet costly task in industrial applications due to the vast number of required real-world tests. Validating such systems by means of simulation…
This paper addresses the complexity of SAT-based invariant inference, a prominent approach to safety verification. We consider the problem of inferring an inductive invariant of polynomial length given a transition system and a safety…
In this paper, we present an efficient algorithm to sample random sparse matrices to be used as check matrices for quantum Low-Density Parity-Check (LDPC) codes. To ease the treatment, we mainly describe our algorithm as a technique to…
We argue that verification of recursive programs by means of the assertional method of C.A.R. Hoare can be conceptually simplified using a modular reasoning. In this approach some properties of the program are established first and…
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…
Most implementations of sampling algorithms for continuous distributions use floating-point numbers, which introduce round-off errors and approximations. These errors can be difficult to analyze, and can cause security issues when used in…
SDE-based methods such as denoising diffusion probabilistic models (DDPMs) have shown remarkable success in real-world sample generation tasks. Prior analyses of DDPMs have been focused on the exponential Euler discretization, showing…