We present an action theory with the power to represent recursive plans and the capability to reason about and synthesize recursive workflow control structures. In contrast with the software verification setting, reasoning does not take place solely over predefined data structures, and neither is there a process specification available in recursive form. Rather, specification takes the form of ...

‎The excessive index of a bridgeless cubic graph $G$ is the least integer $k$‎, ‎such that $G$ can be covered by $k$ perfect matchings‎. ‎An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless‎ ‎cubic graph has excessive index at most five‎. ‎Clearly‎, ‎Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5‎, ‎so Fouquet and Vanherpe as...

It is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfect matchings such that each edge is contained in exactly two of them. Hägglund constructed two graphs Blowup(K4, C) and Blowup(Prism,C4). Based on these two graphs, Chen constructed infinite families of bridgeless cubic graphs M0,1,2,...,k−2,k−1 which is obtained from cyclically 4-edge-connected and having a...

There are many hard conjectures in graph theory, like Tutte’s 5-flow conjecture, and the 5-cycle double cover conjecture, which would be true in general if they would be true for cubic graphs. Since most of them are trivially true for 3-edge-colorable cubic graphs, cubic graphs which are not 3-edge-colorable, often called snarks, play a key role in this context. Here, we survey parameters measu...

Extractability, or “knowledge,” assumptions have recently gained popularity in the cryptographic community, leading to the study of primitives such as extractable one-way functions, extractable hash functions, succinct non-interactive arguments of knowledge (SNARKs), and differing-inputs obfuscation (diO), and spurring the development of a wide spectrum of new applications relying on these prim...

In this report, we aim to present a short description on the Pinocchio which is an efficient solution for Verifiable Computations (VC) and presented by Parno, Howell, Gentry, and Raykova in 2013 IEEE Symposium on Security and Privacy [PHGR13]. In fact, Pinocchio is a practical implementation of SNARKs (Succinct non-interactive argument of knowledge) which are systems that allow a client to ask ...

The total chromatic number χ T (G) is the least number of colours needed to colour the vertices and edges of a graph G, such that no incident or adjacent elements (vertices or edges) receive the same colour. It is known that the problem of determining the total chromatic number is NP-hard and it remains NP-hard even for cubic bipartite graphs. Snarks are simple connected bridgeless cubic graphs...

We present Onion ORAM, an Oblivious RAM (ORAM) with constant worst-case bandwidthblowup that leverages poly-logarithmic server computation to circumvent the logarithmic lowerbound on ORAM bandwidth blowup. Our construction does not require fully homomorphicencryption, but employs an additively homomorphic encryption scheme such as the Damg̊ard-Jurik cryptosystem, or alternatively...

A constrained pseudo random function (PRF) behaves like a standard PRF, but with the added feature that the (master) secret key holder, having secret key K, can produce a constrained key, K{f}, that allows for the evaluation of the PRF on all inputs satisfied by the constraint f . Most existing constrained PRF constructions can handle only bounded length inputs. In a recent work, Abusalah et al...