Related papers: A Verifier Hierarchy
This paper deals with local certification, specifically locally checkable proofs: given a graph property, the task is to certify whether a graph satisfies the property. The verification of this certification needs to be done locally without…
Recently, a plethora of works have proposed inference-time algorithms (e.g. best-of-n), which incorporate verifiers to assist the generation process. Their quality-efficiency trade-offs have been empirically benchmarked on a variety of…
We study the problem of {\sl certification}: given queries to a function $f : \{0,1\}^n \to \{0,1\}$ with certificate complexity $\le k$ and an input $x^\star$, output a size-$k$ certificate for $f$'s value on $x^\star$. This abstractly…
We analyse how the standard reductions between constraint satisfaction problems affect their proof complexity. We show that, for the most studied propositional, algebraic, and semi-algebraic proof systems, the classical constructions of…
We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…
Certificates to a linear algebra computation are additional data structures for each output, which can be used by a---possibly randomized---verification algorithm that proves the correctness of each output. The certificates are essentially…
In this paper, we investigate the problem of verifying the finite-time safety of continuous-time perturbed deterministic systems represented by ordinary differential equations in the presence of measurable disturbances. Given a finite-time…
The paper presents a methodology for temporal logic verification of continuous-time switched stochastic systems. Our goal is to find the lower bound on the probability that a complex temporal property is satisfied over a finite time…
Local certification is a topic originating from distributed computing, where a prover tries to convince the vertices of a graph $G$ that $G$ satisfies some property $\mathcal{P}$. To convince the vertices, the prover gives a small piece of…
We consider leader election in clique networks, where $n$ nodes are connected by point-to-point communication links. For the synchronous clique under simultaneous wake-up, i.e., where all nodes start executing the algorithm in round $1$, we…
Distributed certification, whether it be proof-labeling schemes, locally checkable proofs, etc., deals with the issue of certifying the legality of a distributed system with respect to a given boolean predicate. A certificate is assigned to…
We describe a new algorithm, Minesweeper, that is able to satisfy stronger runtime guarantees than previous join algorithms (colloquially, `beyond worst-case guarantees') for data in indexed search trees. Our first contribution is…
The automation of decision procedures makes certification essential. We suggest to use determinacy of turn-based two-player games with regular winning conditions in order to generate certificates for the number of states that a…
How does one verify that the output of a complicated program is correct? One can formally prove that the program is correct, but this may be beyond the power of existing methods. Alternatively one can check that the output produced for a…
Distributed proofs are mechanisms enabling the nodes of a network to collectivity and efficiently check the correctness of Boolean predicates on the structure of the network, or on data-structures distributed over the nodes (e.g., spanning…
For typical first-order logical theories, satisfying assignments have a straightforward finite representation that can directly serve as a certificate that a given assignment satisfies the given formula. For non-linear real arithmetic…
Chain-of-Thought reasoning has emerged as a powerful approach for solving complex mathematical and logical problems. However, it can often veer off track through incorrect or unsubstantiated inferences. Formal mathematical reasoning, which…
The performance of a reinforcement learning algorithm can vary drastically during learning because of exploration. Existing algorithms provide little information about the quality of their current policy before executing it, and thus have…
Given query access to a monotone function $f\colon\{0,1\}^n\to\{0,1\}$ with certificate complexity $C(f)$ and an input $x^{\star}$, we design an algorithm that outputs a size-$C(f)$ subset of $x^{\star}$ certifying the value of…
We consider temporal logic verification of (possibly nonlinear) dynamical systems evolving over continuous state spaces. Our approach combines automata-based verification and the use of so-called barrier certificates. Automata-based…