7,111 research outputs found
Sublinearly space bounded iterative arrays
Iterative arrays (IAs) are a, parallel computational model with a sequential processing of the input. They are one-dimensional arrays of interacting identical deterministic finite automata. In this note, realtime-lAs with sublinear space bounds are used to accept formal languages. The existence of a proper hierarchy of space complexity classes between logarithmic anel linear space bounds is proved. Furthermore, an optimal spacc lower bound for non-regular language recognition is shown. Key words: Iterative arrays, cellular automata, space bounded computations, decidability questions, formal languages, theory of computatio
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
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EXTEND-L : an input language for extensible register transfer compilation
This report discusses the model and input language for EXTEND, a synthesis system that permits extensible register transfer synthesis. EXTEND-L fills the need for a language that bridges the gap between existing behavioral input descriptions, which are too abstract, and structural schematics, which cannot capture the high-level behavior. The report first discusses previous work in behavioral synthesis and summarizes the deficiencies of these behavioral specifications. The report then describes the proposed langauge in detail, and concludes with a few examples that show its utility
Two computational primitives for algorithmic self-assembly: Copying and counting
Copying and counting are useful primitive operations for computation and construction. We have made DNA crystals that copy and crystals that count as they grow. For counting, 16 oligonucleotides assemble into four DNA Wang tiles that subsequently crystallize on a polymeric nucleating scaffold strand, arranging themselves in a binary counting pattern that could serve as a template for a molecular electronic demultiplexing circuit. Although the yield of counting crystals is low, and per-tile error rates in such crystals is roughly 10%, this work demonstrates the potential of algorithmic self-assembly to create complex nanoscale patterns of technological interest. A subset of the tiles for counting form information-bearing DNA tubes that copy bit strings from layer to layer along their length
How to Color a French Flag--Biologically Inspired Algorithms for Scale-Invariant Patterning
In the French flag problem, initially uncolored cells on a grid must
differentiate to become blue, white or red. The goal is for the cells to color
the grid as a French flag, i.e., a three-colored triband, in a distributed
manner. To solve a generalized version of the problem in a distributed
computational setting, we consider two models: a biologically-inspired version
that relies on morphogens (diffusing proteins acting as chemical signals) and a
more abstract version based on reliable message passing between cellular
agents.
Much of developmental biology research has focused on concentration-based
approaches using morphogens, since morphogen gradients are thought to be an
underlying mechanism in tissue patterning. We show that both our model types
easily achieve a French ribbon - a French flag in the 1D case. However,
extending the ribbon to the 2D flag in the concentration model is somewhat
difficult unless each agent has additional positional information. Assuming
that cells are are identical, it is impossible to achieve a French flag or even
a close approximation. In contrast, using a message-based approach in the 2D
case only requires assuming that agents can be represented as constant size
state machines.
We hope that our insights may lay some groundwork for what kind of message
passing abstractions or guarantees, if any, may be useful in analogy to cells
communicating at long and short distances to solve patterning problems. In
addition, we hope that our models and findings may be of interest in the design
of nano-robots
Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS
Vector Addition Systems with States (VASS) provide a well-known and
fundamental model for the analysis of concurrent processes, parameterized
systems, and are also used as abstract models of programs in resource bound
analysis. In this paper we study the problem of obtaining asymptotic bounds on
the termination time of a given VASS. In particular, we focus on the
practically important case of obtaining polynomial bounds on termination time.
Our main contributions are as follows: First, we present a polynomial-time
algorithm for deciding whether a given VASS has a linear asymptotic complexity.
We also show that if the complexity of a VASS is not linear, it is at least
quadratic. Second, we classify VASS according to quantitative properties of
their cycles. We show that certain singularities in these properties are the
key reason for non-polynomial asymptotic complexity of VASS. In absence of
singularities, we show that the asymptotic complexity is always polynomial and
of the form , for some integer , where is the
dimension of the VASS. We present a polynomial-time algorithm computing the
optimal . For general VASS, the same algorithm, which is based on a complete
technique for the construction of ranking functions in VASS, produces a valid
lower bound, i.e., a such that the termination complexity is .
Our results are based on new insights into the geometry of VASS dynamics, which
hold the potential for further applicability to VASS analysis.Comment: arXiv admin note: text overlap with arXiv:1708.0925
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