Deciding the inequivalence of context-free grammars with 1-letter terminal alphabet is ΣP2-complete

AbstractThis paper deals with the complexity of context-free grammars with 1-letter terminal alphabet. We study the complexity of the membership problem and the inequivalence problem. We show that the first problem is NP-complete and the second one is ΣP2-complete with respect to log-space reduction. The second result also implies that the inequivalence problem is in Pspace, solving an open problem stated by Hunt, Rosenkrantz and Szymanski (1976)

The complexity of equivalence problems for commutative grammars

In this paper we investigate the computational complexity of the inequivalence problems for commutative grammars. We show that the inequivalence problems for type 0 and context-sensitive commutative grammars are undecidable whereas decidability in nondeterministic exponential-time holds for the classes of regular and context-free commutative grammars. For the latter the inequivalence problems are Σp2-hard

Finite-automaton aperiodicity is PSPACE-complete

AbstractIn this paper, we solve an open problem raised by Stern (1985) — “Is finite-automaton aperiodicity PSPACE-complete?” — by providing an affirmative answer. We also characterize the exact complexity of two other problems considered by Stern: (1) dot-depth-one language recognition and (2) piecewise testable language recognition. We show that these two problems are logspace- complete for NL (the class of languages accepted by nondeterministic logspace-bounded Turing machines

Extending Order Preserving Encryption for Multi-User Systems

Several order preserving encryption (OPE) algorithms have been developed in the literature to support search on encrypted data. However, existing OPE schemes only consider a single encryption key, which is infeasible for a practical system with multiple users (implying that all users should have the single encryption key in order to encrypt or decrypt confidential data). In this paper, we develop the first protocols, DOPE and OE-DOPE, to support the use of OPE in multi-user systems. First, we introduce a group of key agents into the system and invent the DOPE protocol to enable “distributed encryption” to assure that the OPE encryption key is not known by any entity in the system. However, in DOPE, if a key agent is compromised, the share of the secret data that is sent to this key agent is compromised. To solve the problem, we developed a novel oblivious encryption (OE) protocol based on the oblivious transfer concept to deliver and encrypt the shares obliviously. Then, we integrate it with DOPE to obtain the OE-DOPE protocol. Security of OE-DOPE is further enhanced with additional techniques. Both DOPE and OE-DOPE can be used with any existing OPE algorithms while retaining all the advantages of OPE without requiring the users to share the single encryption key, making the OPE approach feasible in practical systems

An Outbreak of Severe Infections with Community-Acquired MRSA Carrying the Panton-Valentine Leukocidin Following Vaccination

Background: Infections with community-acquired methicillin-resistant Staphylococcus aureus (CA-MRSA) are emerging worldwide. We investigated an outbreak of severe CA-MRSA infections in children following out-patient vaccination. Methods and Findings: We carried out a field investigation after adverse events following immunization (AEFI) were reported. We reviewed the clinical data from all cases. S. aureus recovered from skin infections and from nasal and throat swabs were analyzed by pulse-field gel electrophoresis, multi locus sequence typing, PCR and microarray. In May 2006, nine children presented with AEFI, ranging from fatal toxic shock syndrome, necrotizing soft tissue infection, purulent abscesses, to fever with rash. All had received a vaccination injection in different health centres in one District of Ho Chi Minh City. Eight children had been vaccinated by the same health care worker (HCW). Deficiencies in vaccine quality, storage practices, or preparation and delivery were not found. Infection control practices were insufficient. CA-MRSA was cultured in four children and from nasal and throat swabs from the HCW. Strains from children and HCW were indistinguishable. All carried the Panton-Valentine leukocidine (PVL), the staphylococcal enterotoxin B gene, the gene complex for staphylococcal-cassette-chromosome mec type V, and were sequence type 59. Strain HCM3A is epidemiologically unrelated to a strain of ST59 prevalent in the USA, althoughthey belong to the same lineage. Conclusions. We describe an outbreak of infections with CA-MRSA in children, transmitted by an asymptomatic colonized HCW during immunization injection. Consistent adherence to injection practice guidelines is needed to prevent CA-MRSA transmission in both in- and outpatient settings

A Superexponential Lower Bound for Gröbner Bases and Church-Rosser Commutative Thue Systems

The complexity of the normal form algorithms which transform a given polynomial ideal basis into a Gröbner basis or a given commutative Thue system into a Church-Rosser system is presently unknown. In this paper we derive a double-exponential lower bound (22") for the production length and cardinality of Church-Rosser commutative Thue systems, and the degree and cardinality of Gröbner bases