On the Hierarchy of Block Deterministic Languages

A regular language is $k$-lookahead deterministic (resp. $k$-block deterministic) if it is specified by a $k$-lookahead deterministic (resp. $k$-block deterministic) regular expression. These two subclasses of regular languages have been respectively introduced by Han and Wood ($k$-lookahead determinism) and by Giammarresi et al. ($k$-block determinism) as a possible extension of one-unambiguous languages defined and characterized by Br\"uggemann-Klein and Wood. In this paper, we study the hierarchy and the inclusion links of these families. We first show that each $k$-block deterministic language is the alphabetic image of some one-unambiguous language. Moreover, we show that the conversion from a minimal DFA of a $k$-block deterministic regular language to a $k$-block deterministic automaton not only requires state elimination, and that the proof given by Han and Wood of a proper hierarchy in $k$-block deterministic languages based on this result is erroneous. Despite these results, we show by giving a parameterized family that there is a proper hierarchy in $k$-block deterministic regular languages. We also prove that there is a proper hierarchy in $k$-lookahead deterministic regular languages by studying particular properties of unary regular expressions. Finally, using our valid results, we confirm that the family of $k$-block deterministic regular languages is strictly included into the one of $k$-lookahead deterministic regular languages by showing that any $k$-block deterministic unary language is one-unambiguous

Verification of PCP-Related Computational Reductions in Coq

We formally verify several computational reductions concerning the Post correspondence problem (PCP) using the proof assistant Coq. Our verifications include a reduction of a string rewriting problem generalising the halting problem for Turing machines to PCP, and reductions of PCP to the intersection problem and the palindrome problem for context-free grammars. Interestingly, rigorous correctness proofs for some of the reductions are missing in the literature

A data preparation approach for cloud storage based on containerized parallel patterns

In this paper, we present the design, implementation, and evaluation of an efficient data preparation and retrieval approach for cloud storage. The approach includes a deduplication subsystem that indexes the hash of each content to identify duplicated data. As a consequence, avoiding duplicated content reduces reprocessing time during uploads and other costs related to outsource data management tasks. Our proposed data preparation scheme enables organizations to add properties such as security, reliability, and cost-efficiency to their contents before sending them to the cloud. It also creates recovery schemes for organizations to share preprocessed contents with partners and end-users. The approach also includes an engine that encapsulates preprocessing applications into virtual containers (VCs) to create parallel patterns that improve the efficiency of data preparation retrieval process. In a study case, real repositories of satellite images, and organizational files were prepared to be migrated to the cloud by using processes such as compression, encryption, encoding for fault tolerance, and access control. The experimental evaluation revealed the feasibility of using a data preparation approach for organizations to mitigate risks that still could arise in the cloud. It also revealed the efficiency of the deduplication process to reduce data preparation tasks and the efficacy of parallel patterns to improve the end-user service experience.This research was supported by "Fondo Sectorial de Investigación para la Educación";, SEP-CONACyT Mexico, through projects 281565 and 285276

Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation

We apply multivariate Lagrange interpolation to synthesize polynomial quantitative loop invariants for probabilistic programs. We reduce the computation of an quantitative loop invariant to solving constraints over program variables and unknown coefficients. Lagrange interpolation allows us to find constraints with less unknown coefficients. Counterexample-guided refinement furthermore generates linear constraints that pinpoint the desired quantitative invariants. We evaluate our technique by several case studies with polynomial quantitative loop invariants in the experiments

Containment and equivalence of weighted automata: Probabilistic and max-plus cases

This paper surveys some results regarding decision problems for probabilistic and max-plus automata, such as containment and equivalence. Probabilistic and max-plus automata are part of the general family of weighted automata, whose semantics are maps from words to real values. Given two weighted automata, the equivalence problem asks whether their semantics are the same, and the containment problem whether one is point-wise smaller than the other one. These problems have been studied intensively and this paper will review some techniques used to show (un)decidability and state a list of open questions that still remain

Undecidable word problem in subshift automorphism groups

This article studies the complexity of the word problem in groups of automorphisms of subshifts. We show in particular that for any Turing degree, there exists a subshift whose automorphism group contains a subgroup whose word problem has exactly this degree

A hierarchical key pre-distribution scheme for fog networks

Security in fog computing is multi-faceted, and one particular challenge is establishing a secure communication channel between fog nodes and end devices. This emphasizes the importance of designing efficient and secret key distribution scheme to facilitate fog nodes and end devices to establish secure communication channels. Existing secure key distribution schemes designed for hierarchical networks may be deployable in fog computing, but they incur high computational and communication overheads and thus consume significant memory. In this paper, we propose a novel hierarchical key pre-distribution scheme based on “Residual Design” for fog networks. The proposed key distribution scheme is designed to minimize storage overhead and memory consumption, while increasing network scalability. The scheme is also designed to be secure against node capture attacks. We demonstrate that in an equal-size network, our scheme achieves around 84% improvement in terms of node storage overhead, and around 96% improvement in terms of network scalability. Our research paves the way for building an efficient key management framework for secure communication within the hierarchical network of fog nodes and end devices. KEYWORDS: Fog Computing, Key distribution, Hierarchical Networks

STAKECUBE: Combining Sharding and Proof-of-Stake to build Fork-free Secure Permissionless Distributed Ledgers

International audienceOur work focuses on the design of a scalable permissionless blockchain in the proof-of-stake setting. In particular, we use a distributed hash table as a building block to set up randomized shards, and then leverage the sharded architecture to validate blocks in an efficient manner. We combine verifiable Byzantine agreements run by shards of stakeholders and a block validation protocol to guarantee that forks occur with negligible probability. We impose induced churn to make shards robust to eclipse attacks, and we rely on the UTXO coin model to guarantee that any stake-holder action is securely verifiable by anyone. Our protocol works against adaptive adversary, and makes no synchrony assumption beyond what is required for the byzantine agreement

On the generalised Ritt problem as a computational problem

The Ritt problem asks if there is an algorithm that tells whether one prime differential ideal is contained in another one if both are given by their characteristic sets. We give several equivalent formulations of this problem. In particular, we show that it is equivalent to testing if a differential polynomial is a zero divisor modulo a radical differential ideal. The technique used in the proof of equivalence yields algorithms for computing a canonical decomposition of a radical differential ideal into prime components and a canonical generating set of a radical differential ideal. Both proposed representations of a radical differential ideal are independent of the given set of generators and can be made independent of the ranking.Comment: 9 page