Related papers: Magic coins are useful for small-space quantum mac…
We introduce Merlin-Arthur (MA) automata where Merlin provides a certificate at the beginning of computation and it is scanned by Arthur before reading the input. We define Merlin-Arthur deterministic, probabilistic, and quantum finite…
We provide two complexity measures that can be used to measure the running time of algorithms to compute multiplications of long integers. The random access machine with unit or logarithmic cost is not adequate for measuring the complexity…
We show that alternating Turing machines, with a novel and natural definition of acceptance, accept precisely the inductive (Pi-1-1) languages. Total alternating machines, that either accept or reject each input, accept precisely the…
Neural networks are being used to improve the probing of the state spaces of many particle systems as approximations to wavefunctions and in order to avoid the recurring sign problem of quantum monte-carlo. One may ask whether the usual…
We address a well-known problem in combinatorics involving the identification of counterfeit coins with a systematic approach. The methodology can be applied to cases where the total number of coins is exceedingly large such that brute…
Quantum money is the task of verifying the validity of banknotes while ensuring that they cannot be counterfeited. Public-key quantum money allows anyone to perform verification, while the private-key setting restricts the ability to verify…
The efficient certification of classically intractable quantum devices has been a central research question for some time. However, to observe a "quantum advantage", it is believed that one does not need to build a large scale universal…
A locally threshold testable language L is a language with the property that for some non negative integers k and l, whether or not a word u is in the language L depends on (1) the prefix and suffix of the word u of length k > 1 and (2) the…
The slowing down of Moore's Law has led to a crisis as the computing workloads of Artificial Intelligence (AI) algorithms continue skyrocketing. There is an urgent need for scalable and energy-efficient hardware catering to the unique…
We present an original model of paraconsistent Turing machines (PTMs), a generalization of the classical Turing machines model of computation using a paraconsistent logic. Next, we briefl y describe the standard models of quantum…
We show that transformer-based large language models are computationally universal when augmented with an external memory. Any deterministic language model that conditions on strings of bounded length is equivalent to a finite automaton,…
We describe a physical implementation of a quantum finite automaton recognizing a well known family of periodic languages. The realization exploits the polarization degree of freedom of single photons and their manipulation through linear…
Instead of producing quantum languages that are fit for current quantum computers, we build a language from standard classical assembler and augment it with quantum capabilities so that quantum algorithms become a subset of it. This paves…
We investigate the correspondence between the time and space recognition complexity of languages. For this purpose, we will code the long-continued computations of deterministic two-tape Turing machines by the relatively short-length…
For decades it is known that Quantum Computers might serve as a tool to solve a very specific kind of problems that have long thought to be incalculable. Some of those problems are of a combinatorial nature, with the quantum advantage…
A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is…
The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. In this work, we look at the same idea of "recognizability by finite monoids" for other monoids. In particular, we attempt to…
We introduce an affine generalization of counter automata, and analyze their ability as well as affine finite automata. Our contributions are as follows. We show that there is a language that can be recognized by exact realtime affine…
Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by…
QBism regards quantum mechanics as an addition to probability theory. The addition provides an extra normative rule for decision-making agents concerned with gambling across experimental contexts, somewhat in analogy to the double-slit…