Related papers: Certificates in Data Structures
In this dissertation, we study two of the global properties of 1-dimensional cellular automata (CAs) under periodic boundary condition, namely, reversibility and randomness. To address reversibility of finite CAs, we develop a mathematical…
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…
In unitary property testing a quantum algorithm, also known as a tester, is given query access to a black-box unitary and has to decide whether it satisfies some property. We propose a new technique for proving lower bounds on the quantum…
We construct efficient data structures that are resilient against a constant fraction of adversarial noise. Our model requires that the decoder answers most queries correctly with high probability and for the remaining queries, the decoder…
We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\mathcal{P}$, the goal is to distinguish between…
Local certification is a mechanism for certifying to the nodes of a network that a certain property holds. In this framework, nodes are assigned labels, called certificates, which are supposed to prove that the property holds. The nodes…
Many problems in interprocedural program analysis can be modeled as the context-free language (CFL) reachability problem on graphs and can be solved in cubic time. Despite years of efforts, there are no known truly sub-cubic algorithms for…
Certified robustness circumvents the fragility of defences against adversarial attacks, by endowing model predictions with guarantees of class invariance for attacks up to a calculated size. While there is value in these certifications, the…
We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish…
In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy,…
We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…
A memory-efficient framework is described for the cardinality-constrained structured data-fitting problem. Dual-based atom-identification rules are proposed that reveal the structure of the optimal primal solution from near-optimal dual…
Can easy sets only have easy certificate schemes? In this paper, we study the class of sets that, for all NP certificate schemes (i.e., NP machines), always have easy acceptance certificates (i.e., accepting paths) that can be computed in…
We investigate the probabilistic feasibility of randomized solutions to two distinct classes of uncertain multi-agent optimization programs. We first assume that only the constraints of the program are affected by uncertainty, while the…
Model counting, or counting the satisfying assignments of a Boolean formula, is a fundamental problem with diverse applications. Given #P-hardness of the problem, developing algorithms for approximate counting is an important research area.…
We study the {\em verification} problem in distributed networks, stated as follows. Let $H$ be a subgraph of a network $G$ where each vertex of $G$ knows which edges incident on it are in $H$. We would like to verify whether $H$ has some…
Memory consistency models (MCMs) are at the heart of concurrent programming. They represent the behaviour of concurrent programs at the chip level. To test these models small program snippets called litmus test are generated, which show…
We resolve the long-standing open problem of Boolean dynamic data structure hardness, proving an unconditional lower bound of $\Omega((\log n / \log\log n)^2)$ for the Multiphase Problem of Patrascu [STOC 2010] (instantiated with Inner…
The two-sample hypothesis testing problem is studied for the challenging scenario of high dimensional data sets with small sample sizes. We show that the two-sample hypothesis testing problem can be posed as a one-class set classification…
Barrier certificates, serving as differential invariants that witness system safety, play a crucial role in the verification of cyber-physical systems (CPS). Prevailing computational methods for synthesizing barrier certificates are based…