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In this paper, we consider the computational complexity of formally verifying the behavior of Rectified Linear Unit (ReLU) Neural Networks (NNs), where verification entails determining whether the NN satisfies convex polytopic…

We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By "accurate" we mean that the computed…

This article aims to describe and explain the theoretical foundations of concurrent and set concurrent algorithms, considering an asynchronous shared memory system where any number of processes can crash. Verification of concurrent…

Most proof systems for concurrent programs assume the underlying memory model to be sequentially consistent (SC), an assumption which does not hold for modern multicore processors. These processors, for performance reasons, implement…

Two matrices are said to be principal minor equivalent if they have equal corresponding principal minors of all orders. We give a characterization of principal minor equivalence and a deterministic polynomial time algorithm to check if two…

Linearizability has become the de facto correctness specification for implementations of concurrent data structures. While formally verifying such implementations remains challenging, linearizability monitoring has emerged as a promising…

Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…

In this paper we solve on GPUs massive problems with large amount of data, which are not appropriate for solution with the SIMD technology. For the given problem we consider a three-level parallelization. The multithreading of CPU is used…

Multiprocessor task scheduling is an important and computationally difficult problem. This paper proposes a comparison study of genetic algorithm and list scheduling algorithm. Both algorithms are naturally parallelizable but have heavy…

The memory model of a shared-memory multiprocessor is a contract between the designer and programmer of the multiprocessor. The sequential consistency memory model specifies a total order among the memory (read and write) events performed…

P-time event graphs are discrete event systems able to model cyclic production systems where tasks need to be performed within given time windows. Consistency is the property of admitting an infinite execution of such tasks that does not…

This paper proposes a thought experiment to search for efficient bounded algorithms of NPC problems by machine enumeration. The key contributions are: -- On Universal Turing Machines, a program's time complexity should be characterized as:…

Sequential computation is well understood but does not scale well with current technology. Within the next decade, systems will contain large numbers of processors with potentially thousands of processors per chip. Despite this, many…

The transition from single-core to multi-core processors has made multi-threaded software an important subject in computer aided verification. Here, we describe and evaluate an extension of the ESBMC model checker to support the…

A key computational question underpinning the automated testing and verification of concurrent programs is the consistency question - given a partial execution history, can it be completed in a consistent manner? Due to its importance,…

The Kernel Polynomial Method (KPM) is one of the fast diagonalization methods used for simulations of quantum systems in research fields of condensed matter physics and chemistry. The algorithm has a difficulty to be parallelized on a…

We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…

Multithreaded programs generally leverage efficient and thread-safe concurrent objects like sets, key-value maps, and queues. While some concurrent-object operations are designed to behave atomically, each witnessing the atomic effects of…

We present algorithms for checking and enforcing robustness of concurrent programs against the Total Store Ordering (TSO) memory model. A program is robust if all its TSO computations correspond to computations under the Sequential…

Runtime verification is checking whether a system execution satisfies or violates a given correctness property. A procedure that automatically, and typically on the fly, verifies conformance of the system's behavior to the specified…