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With the advent of high-performance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in…

Proving complexity lower bounds remains a challenging task: we only know how to prove conditional uniform lower bounds and nonuniform lower bounds in restricted circuit models. Williams (STOC 2010) showed how to derive nonuniform lower…

Membrane computing and P systems are a paradigm of massively parallel natural computing introduced by Gheorghe P\u{a}un in 1999, inspired by the structure of the living cell and by its biochemical reactions. In spite of this explicit…

Memory consistency models define the order in which accesses to shared memory in a concurrent system may be observed to occur. Such models are a necessity since program order is not a reliable indicator of execution order, due to…

We consider a class of systems over finite alphabets, namely discrete-time systems with linear dynamics and a finite input alphabet. We formulate a notion of finite uniform bisimulation, and motivate and propose a notion of regular finite…

In this work, we initiate the study of the Minimum Circuit Size Problem (MCSP) in the quantum setting. MCSP is a problem to compute the circuit complexity of Boolean functions. It is a fascinating problem in complexity theory -- its…

Entanglement membrane theory is an effective coarse-grained description of entanglement dynamics and operator growth in chaotic quantum many-body systems. The fundamental quantity characterizing the membrane is the entanglement line…

Boolean and quantum circuits have commonalities and differences. To formalize the syntactical commonality we introduce syntactic circuits where the gates are black boxes. Syntactic circuits support various semantics. One semantics is…

Many NP-complete problems take integers as part of their input instances. These input integers are generally binarized, that is, provided in the form of the "binary" numeral representation, and the lengths of such binary forms are used as a…

Universal memcomputing machines (UMMs) [IEEE Trans. Neural Netw. Learn. Syst. 26, 2702 (2015)] represent a novel computational model in which memory (time non-locality) accomplishes both tasks of storing and processing of information. UMMs…

Dedicated analog neurocomputing circuits are promising for high-throughput, low power consumption applications of machine learning (ML) and for applications where implementing a digital computer is unwieldy (remote locations; small, mobile,…

Data representation is crucial for the success of machine learning models. In the context of quantum machine learning with near-term quantum computers, equally important considerations of how to efficiently input (encode) data and…

Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary…

The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…

We consider the power of Boolean circuits with MOD$_{6}$ gates. First, we introduce a few basic notions of computational complexity, and describe the standard models with which we study the complexity of problems. We then define the model…

Computational spectral imaging is drawing increasing attention owing to the snapshot advantage, and amplitude, phase, and wavelength encoding systems are three types of representative implementations. Fairly comparing and understanding the…

Membrane systems represent a computational model that operates in a distributed and parallel manner, inspired by the behavior of biological cells. These systems feature objects that transform within a nested membrane structure. This…

Weak-memory models are standard formal specifications of concurrency across hardware, programming languages, and distributed systems. A fundamental computational problem is consistency testing: is the observed execution of a concurrent…

In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the…

Multiprocess systems, including grid systems, multiprocessors and multicore computers, incorporate a variety of specialized hardware and software mechanisms, which speed computation, but result in complex memory behavior. As a consequence,…