10,527 research outputs found
Descriptional complexity of cellular automata and decidability questions
We study the descriptional complexity of cellular automata (CA), a parallel model of computation. We show that between one of the simplest cellular models, the realtime-OCA. and "classical" models like deterministic finite automata (DFA) or pushdown automata (PDA), there will be savings concerning the size of description not bounded by any recursive function, a so-called nonrecursive trade-off. Furthermore, nonrecursive trade-offs are shown between some restricted classes of cellular automata. The set of valid computations of a Turing machine can be recognized by a realtime-OCA. This implies that many decidability questions are not even semi decidable for cellular automata. There is no pumping lemma and no minimization algorithm for cellular automata
On non-recursive trade-offs between finite-turn pushdown automata
It is shown that between one-turn pushdown automata (1-turn PDAs) and deterministic finite automata (DFAs) there will be savings concerning the size of description not bounded by any recursive function, so-called non-recursive tradeoffs. Considering the number of turns of the stack height as a consumable resource of PDAs, we can show the existence of non-recursive trade-offs between PDAs performing k+ 1 turns and k turns for k >= 1. Furthermore, non-recursive trade-offs are shown between arbitrary PDAs and PDAs which perform only a finite number of turns. Finally, several decidability questions are shown to be undecidable and not semidecidable
On the descriptional complexity of iterative arrays
The descriptional complexity of iterative arrays (lAs) is studied. Iterative arrays are a parallel computational model with a sequential processing of the input. It is shown that lAs when compared to deterministic finite automata or pushdown automata may provide savings in size which are not bounded by any recursive function, so-called non-recursive trade-offs. Additional non-recursive trade-offs are proven to exist between lAs working in linear time and lAs working in real time. Furthermore, the descriptional complexity of lAs is compared with cellular automata (CAs) and non-recursive trade-offs are proven between two restricted classes. Finally, it is shown that many decidability questions for lAs are undecidable and not semidecidable
On one-way cellular automata with a fixed number of cells
We investigate a restricted one-way cellular automaton (OCA) model where the number of cells is bounded by a constant number k, so-called kC-OCAs. In contrast to the general model, the generative capacity of the restricted model is reduced to the set of regular languages. A kC-OCA can be algorithmically converted to a deterministic finite automaton (DFA). The blow-up in the number of states is bounded by a polynomial of degree k. We can exhibit a family of unary languages which shows that this upper bound is tight in order of magnitude. We then study upper and lower bounds for the trade-off when converting DFAs to kC-OCAs. We show that there are regular languages where the use of kC-OCAs cannot reduce the number of states when compared to DFAs. We then investigate trade-offs between kC-OCAs with different numbers of cells and finally treat the problem of minimizing a given kC-OCA
Towards a Holistic Integration of Spreadsheets with Databases: A Scalable Storage Engine for Presentational Data Management
Spreadsheet software is the tool of choice for interactive ad-hoc data
management, with adoption by billions of users. However, spreadsheets are not
scalable, unlike database systems. On the other hand, database systems, while
highly scalable, do not support interactivity as a first-class primitive. We
are developing DataSpread, to holistically integrate spreadsheets as a
front-end interface with databases as a back-end datastore, providing
scalability to spreadsheets, and interactivity to databases, an integration we
term presentational data management (PDM). In this paper, we make a first step
towards this vision: developing a storage engine for PDM, studying how to
flexibly represent spreadsheet data within a database and how to support and
maintain access by position. We first conduct an extensive survey of
spreadsheet use to motivate our functional requirements for a storage engine
for PDM. We develop a natural set of mechanisms for flexibly representing
spreadsheet data and demonstrate that identifying the optimal representation is
NP-Hard; however, we develop an efficient approach to identify the optimal
representation from an important and intuitive subclass of representations. We
extend our mechanisms with positional access mechanisms that don't suffer from
cascading update issues, leading to constant time access and modification
performance. We evaluate these representations on a workload of typical
spreadsheets and spreadsheet operations, providing up to 20% reduction in
storage, and up to 50% reduction in formula evaluation time
Equivalence-based Security for Querying Encrypted Databases: Theory and Application to Privacy Policy Audits
Motivated by the problem of simultaneously preserving confidentiality and
usability of data outsourced to third-party clouds, we present two different
database encryption schemes that largely hide data but reveal enough
information to support a wide-range of relational queries. We provide a
security definition for database encryption that captures confidentiality based
on a notion of equivalence of databases from the adversary's perspective. As a
specific application, we adapt an existing algorithm for finding violations of
privacy policies to run on logs encrypted under our schemes and observe low to
moderate overheads.Comment: CCS 2015 paper technical report, in progres
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