Related papers: Energy Complexity of Regular Languages
The energy cost of erasing quantum states depends on our knowledge of the states. We show that learning algorithms can acquire such knowledge to erase many copies of an unknown state at the optimal energy cost. This is proved by showing…
We realize constant-space quantum computation by measure-many two-way quantum finite automata and evaluate their language recognition power by analyzing patterns of their exotic behaviors and by exploring their structural properties. In…
Reversible forms of computations are often interesting from an energy efficiency point of view. When the computation device in question is an automaton, it is known that the minimal reversible automaton recognizing a given language is not…
We prove the following facts about the language recognition power of quantum Turing machines (QTMs) in the unbounded error setting: QTMs are strictly more powerful than probabilistic Turing machines for any common space bound $ s $…
We introduce and investigate forgetting 1-limited automata, which are single-tape Turing machines that, when visiting a cell for the first time, replace the input symbol in it by a fixed symbol, so forgetting the original contents. These…
It is now well established that there is no lower bound for the energy dissipated during a computation. The relevance of the zero-energy limit is unclear, however, because it entails computations that are unreliable or infinitely slow, or…
The theory of computation is based on abstract computing automata which can be classified into a three-class hierarchy: Finite Automata (FA), Push-down Automata (PDA) and the Turing Machines (TM). Each class corresponds to grammar/language…
Turing Machines (TMs) are the canonical model of computation in computer science and physics. We combine techniques from algorithmic information theory and stochastic thermodynamics to analyze the thermodynamic costs of TMs. We consider two…
While it has been widely recognized that genuine quantum advantage for practical problems might only be achieved with fault-tolerant quantum computers, it is still not entirely clear whether the required quantum error correction will be…
The Landauer principle bridges the energetic cost and information processing, showing that irreversible computation inevitably demands energy dissipation. As energy demands from computation continue to rise, approximate computing has…
We outline the construction of a molecular system that could, in principle, implement a thermodynamically reversible Universal Turing Machine (UTM). By proposing a concrete-albeit idealised-design and operational protocol, we reveal…
Quantum error correcting codes can be cast in a way which is strikingly similar to a quantum heat engine undergoing an Otto cycle. In this paper we strengthen this connection further by carrying out a complete assessment of the…
Since reversible computing requires preservation of all information throughout the entire computational process, this implies that all errors that appear as a result of the interaction of the information-carrying system with uncontrolled…
The erasure of information is fundamentally an irreversible logical operation, carrying profound consequences for the energetics of computation and information processing. We investigate the thermodynamic costs associated with erasing (and…
The fundamental energy cost of irreversible computing is given by the Landauer bound of $kT \ln2$~/bit. However, this limit is only achievable for infinite-time processes. We here determine the fundamental energy cost of finite-time…
We examine the characteristic features of reversible and quantum computations in the presence of supplementary external information, known as advice. In particular, we present a simple, algebraic characterization of languages recognized by…
Deterministic synchronous systems consisting of two finite automata running in opposite directions on a shared read-only input are studied with respect to their ability to perform reversible computations, which means that the automata are…
Developing a thermodynamic theory of computation is a challenging task at the interface of non-equilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times,…
Perfectly rational decision-makers maximize expected utility, but crucially ignore the resource costs incurred when determining optimal actions. Here we propose an information-theoretic formalization of bounded rational decision-making…
Real-world computers have operational constraints that cause nonzero entropy production (EP). In particular, almost all real-world computers are ``periodic'', iteratively undergoing the same physical process; and ``local", in that…