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We study the weakest model of quantum nondeterminism in which a classical proof has to be checked with probability one by a quantum protocol. We show the first separation between classical nondeterministic communication complexity and this…
We argue that Godel's completeness theorem is equivalent to completability of consistent theories, and Godel's incompleteness theorem is equivalent to the fact that this completion is not constructive, in the sense that there are some…
In this paper we study quantum nondeterminism in multiparty communication. There are three (possibly) different types of nondeterminism in quantum computation: i) strong, ii) weak with classical proofs, and iii) weak with quantum proofs.…
Latent Chain-of-Thought (Latent CoT) models promise efficient reasoning via continuous representations, yet exhibit puzzling performance inconsistencies: excelling at exploration (ProsQA: 97.0%) but failing at computation (GSM8K: 34.1%). We…
Bell's 1964 theorem, which states that the predictions of quantum theory cannot be accounted for by any local theory, represents one of the most profound developments in the foundations of physics. In the last two decades, Bell's theorem…
We study monads resulting from the combination of nondeterministic and probabilistic behaviour with the possibility of termination, which is essential in program semantics. Our main contributions are presentation results for the monads,…
This article discusses completeness of Boolean Algebra as First Order Theory in Goedel's meaning. If Theory is complete then any possible transformation is equivalent to some transformation using axioms, predicates etc. defined for this…
We propose a decision-theoretic framework for computational complexity, complementary to classical theory: moving from syntactic exactness (Turing / Shannon) to semantic simulability (Le Cam). While classical theory classifies problems by…
The ability to reason under uncertainty and with incomplete information is a fundamental requirement of decision support technology. In this paper we argue that the concentration on theoretical techniques for the evaluation and selection of…
The paper explores known results related to the problem of identifying if a given program terminates on all inputs -- this is a simple generalization of the halting problem. We will see how this problem is related and the notion of proof…
Does the notion of a quantum randomized or nondeterministic algorithm make sense, and if so, does quantum randomness or nondeterminism add power? Although reasonable quantum random sources do not add computational power, the discussion of…
We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…
Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {\em need not} be a Turing machine and,…
The interface between classical physics and quantum physics is explained from the point of view of quantum information theory (Feynman Processes). The interpretation depends on a hefty sacrifice: the classical determinism or the arrow of…
Quantum computers take advantage of interfering quantum alternatives in order to handle problems that might be too time consuming with algorithms based on classical logic. Developing quantum computers requires new ways of thinking beyond…
Quantum theory has an epistemic horizon, i.e. exact values cannot be assigned simultaneously to incompatible physical quantities. As shown by Spekkens' toy theory, positing an epistemic horizon akin to Heisenberg's uncertainty principle in…
Though many safety-critical software systems use floating point to represent real-world input and output, programmers usually have idealized versions in mind that compute with real numbers. Significant deviations from the ideal can cause…
Methods to find counterfactual explanations have predominantly focused on one step decision making processes. In this work, we initiate the development of methods to find counterfactual explanations for decision making processes in which…
This paper is devoted to the complexity of the Boolean satisfiability problem. We consider a version of this problem, where the Boolean formula is specified in the conjunctive normal form. We prove an unexpected result that the…
We investigate the decidability of model-checking logics of time, knowledge and probability, with respect to two epistemic semantics: the clock and synchronous perfect recall semantics in partially observed discrete-time Markov chains.…