Related papers: Local Reasoning about Probabilistic Behaviour for …
Quantum computational logics represent a logical abstraction from the circuit-theory in quantum computation. In these logics formulas are supposed to denote pieces of quantum information (qubits, quregisters or mixtures of quregisters),…
While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…
Proof theory provides a foundation for studying and reasoning about programming languages, most directly based on the well-known Curry-Howard isomorphism between intuitionistic logic and the typed lambda-calculus. More recently, a…
We show how automatic tools for the verification of linear and branching time properties of procedural, multi-threaded, and functional programs as well as program synthesis can be naturally and uniformly seen as solvers of constraints in…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
Abstract interpretation, Hoare logic, and incorrectness (or reverse Hoare) logic are powerful techniques for static analysis of computer programs. All of them have been successfully extended to the quantum setting, but largely developed in…
Many natural program correctness properties can be stated in terms of symmetries, but existing formal methods have little support for reasoning about such properties. We consider how to formally verify a broad class of symmetry properties…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate.Moreover, to model concurrent and…
Counting propositional logic was recently introduced in relation to randomized computation and shown able to logically characterize the full counting hierarchy. In this paper we aim to clarify the intuitive meaning and expressive power of…
We present the first protocol allowing a classical computer to interactively verify the result of an efficient quantum computation. We achieve this by constructing a measurement protocol, which enables a classical verifier to use a quantum…
A hybrid quantum-classical algorithm is a computational scheme in which quantum circuits are used to extract information that is then processed by a classical routine to guide subsequent quantum operations. These algorithms are especially…
We demonstrate that locally connected networks of machines that have primitive learning capabilities can be used to perform a deterministic, event-based simulation of quantum computation. We present simulation results for basic quantum…
We describe how a probabilistic Hoare logic with localities can be used for reasoning about security. As a proof-of-concept, we analyze Vernam and El-Gamal cryptosystems, prove the security properties that they do satisfy and disprove those…
Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…
The aim of this paper is to apply a contextual probabilistic model (in the spirit of Mackey, Gudder, Ballentine) to represent and to generalize some results of quantum logic about possible macroscopic quantum-like (QL) behaviour. The…
We demonstrate that behavioral probabilities of human decision makers share many common features with quantum probabilities. This does not imply that humans are some quantum objects, but just shows that the mathematics of quantum theory is…
The quantum theory (QT) and new stochastic approaches have no deterministic prediction for a single measurement or for a single time -series of events observed for a trapped ion, electron or any other individual physical system. The…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…
Quantum computing exhibits the unique capability to natively and efficiently encode various natural phenomena, promising theoretical speedups of several orders of magnitude. However, not all computational tasks can be efficiently executed…