Related papers: Efficiently Batching Unambiguous Interactive Proof…
Let L be a language decided by a constant-round quantum Arthur-Merlin (QAM) protocol with negligible soundness error and all but possibly the last message being classical. We prove that if this protocol is zero knowledge with a black-box,…
Hardness amplification is a central problem in the study of interactive protocols. While ``natural'' parallel repetition transformation is known to reduce the soundness error of some special cases of interactive arguments: three-message…
We consider zero knowledge interactive proofs in a richer, more realistic communication environment. In this setting, one may simultaneously engage in many interactive proofs, and these proofs may take place in an asynchronous fashion. It…
The study of distributed interactive proofs was initiated by Kol, Oshman, and Saxena [PODC 2018] as a generalization of distributed decision mechanisms (proof-labeling schemes, etc.), and has received a lot of attention in recent years. In…
Complexity class containments involving interactive proof classes are famously nonrelativizing: although $\mathsf{IP} = \mathsf{PSPACE}$, Fortnow and Sipser showed that that there exists an oracle relative to which $\mathsf{coNP}…
We use results from communication complexity, both new and old ones, to prove lower bounds for unambiguous finite automata (UFAs). We show three results. $\textit{Complement:}$ There is a language $L$ recognised by an $n$-state UFA such…
In two-prover one-round interactive proof systems, no-signaling provers are those who are allowed to use arbitrary strategies, not limited to local operations, as long as their strategies cannot be used for communication between them. Study…
We give new proofs of soundness (all representable functions on base types lies in certain complexity classes) for Elementary Affine Logic, LFPL (a language for polytime computation close to realistic functional programming introduced by…
This survey provides a comprehensive examination of verifiable computing, tracing its evolution from foundational complexity theory to modern zero-knowledge succinct non-interactive arguments of knowledge (ZK-SNARKs). We explore key…
Probabilistic Logic Programming (PLP) languages, like ProbLog, naturally support reasoning under uncertainty, while maintaining a declarative and interpretable framework. Meanwhile, counterfactual reasoning (i.e., answering ``what if''…
The mixedness of one share of a pure bipartite state determines whether the overall state is a separable, unentangled state. Here we consider quantum computational tests of mixedness, and we derive an exact expression of the acceptance…
Alice and Bob want to run a protocol over a noisy channel, where a certain number of bits are flipped adversarially. Several results take a protocol requiring $L$ bits of noise-free communication and make it robust over such a channel. In a…
LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…
We continue the study of doubly-efficient proof systems for verifying agnostic PAC learning, for which we obtain the following results. - We construct an interactive protocol for learning the $t$ largest Fourier characters of a given…
In \cite{Craig}, we introduced a syntactically defined and highly general class of calculi known as \emph{semi-analytic}. We then demonstrated that any sufficiently strong (modal) substructural logic with a semi-analytic calculus must…
Two dual questions in quantum information theory are to determine the communication cost of simulating a bipartite unitary gate, and to determine their communication capacities. We present a bipartite unitary gate with two surprising…
Using the measurement-based quantum computation model, we construct interactive proofs with non-communicating quantum provers and a classical verifier. Our construction gives interactive proofs for all languages in BQP with a polynomial…
We consider the problem of implementing two-party interactive quantum communication over noisy channels, a necessary endeavor if we wish to fully reap quantum advantages for communication. For an arbitrary protocol with $n$ messages,…
Cross-lingual chain-of-thought (XCoT) with self-consistency markedly enhances multilingual reasoning, yet existing methods remain costly due to extensive sampling of full trajectories across languages. Moreover, multilingual LLM…
We analyze quantum two prover one round interactive proof systems, in which noninteracting provers can share unlimited entanglement. The maximum acceptance probability is characterized as a superoperator norm. We get some partial results…