Related papers: Deciding Indistinguishability
A physical system is determined by a finite set of initial conditions and "laws" represented by equations. The system is computable if we can solve the equations in all instances using a "finite body of mathematical knowledge". In this…
Value independence is enormously beneficial for reasoning about software systems at scale. These benefits carry over into the world of formal verification. Reasoning about programs algebraically is a simple affair in a proof assistant,…
The rewriting system sigma is the set of rules propagating explicit substitutions in the lambda-calculus with explicit substitutions. In this note, we prove the undecidability of unification modulo sigma.
Causality serves as an abstract notion of time for concurrent systems. A computation is causal, or simply valid, if each observation of a computation event is preceded by the observation of its causes. The present work establishes that this…
Unclonable encryption, first introduced by Broadbent and Lord (TQC'20), is a one-time encryption scheme with the following security guarantee: any non-local adversary (A, B, C) cannot simultaneously distinguish encryptions of two equal…
In a previous paper, we provided a formal definition for the concept of computational irreducibility (CIR), i.e. the fact for a function f from N to N that it is impossible to compute f(n) without following approximately the same path than…
I survey recent progress on a classic and challenging problem in social choice: the fair division of indivisible items. I discuss how a computational perspective has provided interesting insights into and understanding of how to divide…
We consider first-order logic over the subword ordering on finite words, where each word is available as a constant. Our first result is that the $\Sigma_1$ theory is undecidable (already over two letters). We investigate the decidability…
We explore several concepts for analyzing the intuitive notion of computational irreducibility and we propose a robust formal definition, first in the field of cellular automata and then in the general field of any computable function f…
Dependent Object Types (DOT) is a calculus with path dependent types, intersection types, and object self-references, which serves as the core calculus of Scala 3. Although the calculus has been proven sound, it remains open whether type…
The problem of distinguishing two unitary transformations, or quantum gates, is analyzed and a function reflecting their statistical distinguishability is found. Given two unitary operations, $U_1$ and $U_2$, it is proved that there always…
The performance of a quantum information processing protocol is ultimately judged by distinguishability measures that quantify how distinguishable the actual result of the protocol is from the ideal case. The most prominent…
A cryptographic protocol (CP) is a distributed algorithm designed to provide a secure communication in an insecure environment. CPs are used, for example, in electronic payments, electronic voting procedures, database access systems, etc.…
Computation is commonly defined as the execution of abstract algorithms over symbolic representations, with physical systems treated as substrates that realise predefined operations. While effective for engineered machines, this separation…
Higher-order processes with parameterization are capable of abstraction and application (migrated from the lambda-calculus), and thus are computationally more expressive. For the minimal higher-order concurrency, it is well-known that the…
Typical elements of quantum networks are made by identical systems, which are the basic particles constituting a resource for quantum information processing. Whether the indistinguishability due to particle identity is an exploitable…
Computability logic (CoL) is a formal theory of interactive computation. It understands computational problems as games played by two players: a machine and its environment, uses logical formalism to describe valid principles of…
This work initiates an analysis of several cryptographic protocols from a rational point of view using a game-theoretical approach, which allows us to represent not only the protocols but also possible misbehaviours of parties. Concretely,…
This paper delves into the intersection of computational theory and music, examining the concept of undecidability and its significant, yet overlooked, implications within the realm of modern music composition and production. It posits that…
Game semantics aim at describing the interactive behaviour of proofs by interpreting formulas as games on which proofs induce strategies. In this article, we introduce a game semantics for a fragment of first order propositional logic. One…