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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.
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.
The effect of adding two-way communication to k cells one-way cellular automata (kC-OCAs) on their size of description is studied. kC-OCAs are a parallel model for the regular languages that consists of an array of k identical deterministic finite automata (DFAs), called cells, operating in parallel. Each cell gets information from its right neighbor only. In this paper, two models with different amounts of two-way communication are investigated. Both models always achieve quadratic savings when compared to DFAs. When compared to a one-way cellular model, the result is that minimum two-way communication can achieve at most quadratic savings whereas maximum two-way communication may provide savings bounded by a polynomial of degree k.
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.
It is known that deterministic finite automata (DFAs) can be algorithmically minimized, i.e., a DFA M can be converted to an equivalent DFA M' which has a minimal number of states. The minimization can be done efficiently [6]. On the other hand, it is known that unambiguous finite automata (UFAs) and nondeterministic finite automata (NFAs) can be algorithmically minimized too, but their minimization problems turn out to be NP-complete and PSPACE-complete [8]. In this paper, the time complexity of the minimization problem for two restricted types of finite automata is investigated. These automata are nearly deterministic, since they only allow a small amount of non determinism to be used. On the one hand, NFAs with a fixed finite branching are studied, i.e., the number of nondeterministic moves within every accepting computation is bounded by a fixed finite number. On the other hand, finite automata are investigated which are essentially deterministic except that there is a fixed number of different initial states which can be chosen nondeterministically. The main result is that the minimization problems for these models are computationally hard, namely NP-complete. Hence, even the slightest extension of the deterministic model towards a nondeterministic one, e.g., allowing at most one nondeterministic move in every accepting computation or allowing two initial states instead of one, results in computationally intractable minimization problems.
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.
We propose a variation of online paging in two-level memory systems where pages in the fast cache get modified and therefore have to be explicitly written back to the slow memory upon evictions. For increased performance, up to alpha arbitrary pages can be moved from the cache to the slow memory within a single joint eviction, whereas fetching pages from the slow memory is still performed on a one-by-one basis. The main objective in this new alpha-paging scenario is to bound the number of evictions. After providing experimental evidence that alpha-paging can adequately model flash-memory devices in the context of translation layers we turn to the theoretical connections between alpha-paging and standard paging. We give lower bounds for deterministic and randomized alpha-paging algorithms. For deterministic algorithms, we show that an adaptation of LRU is strongly competitive, while for the randomized case we show that by adapting the classical Mark algorithm we get an algorithm with a competitive ratio larger than the lower bound by a multiplicative factor of approximately 1.7.
FIFO is the most prominent queueing strategy due to its simplicity and the fact that it only works with local information. Its analysis within the adversarial queueing theory however has shown, that there are networks that are not stable under the FIFO protocol, even at arbitrarily low rate. On the other hand there are networks that are universally stable, i.e., they are stable under every greedy protocol at any rate r < 1. The question as to which networks are stable under the FIFO protocol arises naturally. We offer the first polynomial time algorithm for deciding FIFO stability and simple-path FIFO stability of a directed network, answering an open question posed in [1, 4]. It turns out, that there are networks, that are FIFO stable but not universally stable, hence FIFO is not a worst case protocol in this sense. Our characterization of FIFO stability is constructive and disproves an open characterization in [4].
The efficient management of large multimedia databases requires the development of new techniques to process, characterize, and search for multimedia objects. Especially in the case of image data, the rapidly growing amount of documents prohibits a manual description of the images’ content. Instead, the automated characterization is highly desirable to support annotation and retrieval of digital images. However, this is a very complex and still unsolved task. To contribute to a solution of this problem, we have developed a mechanism for recognizing objects in images based on the query by example paradigm. Therefore, the most salient image features of an example image representing the searched object are extracted to obtain a scale-invariant object model. The use of this model provides an efficient and robust strategy for recognizing objects in images independently of their size. Further applications of the mechanism are classical recognition tasks such as scene decomposition or object tracking in video sequences.
Classically, encoding of images by only a few, important components is done by the Principal Component Analysis (PCA). Recently, a data analysis tool called Independent Component Analysis (ICA) for the separation of independent influences in signals has found strong interest in the neural network community. This approach has also been applied to images. Whereas the approach assumes continuous source channels mixed up to the same number of channels by a mixing matrix, we assume that images are composed by only a few image primitives. This means that for images we have less sources than pixels. Additionally, in order to reduce unimportant information, we aim only for the most important source patterns with the highest occurrence probabilities or biggest information called „Principal Independent Components (PIC)“. For the example of a synthetic picture composed by characters this idea gives us the most important ones. Nevertheless, for natural images where no a-priori probabilities can be computed this does not lead to an acceptable reproduction error. Combining the traditional principal component criteria of PCA with the independence property of ICA we obtain a better encoding. It turns out that this definition of PIC implements the classical demand of Shannon’s rate distortion theory.