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 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 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

Managing the KM Trade-Off: Knowledge Centralization versus Distribution

KM is more an archipelago of theories and practices rather than a monolithic approach. We propose a conceptual map that organizes some major approaches to KM according to their assumptions on the nature of knowledge. The paper introduces the two major views on knowledge ­objectivist, subjectivist - and explodes each of them into two major approaches to KM: knowledge as a market, and knowledge as intellectual capital (the objectivistic perspective); knowledge as mental models, and knowledge as practice (the subjectivist perspective). We argue that the dichotomy between objective and subjective approaches is intrinsic to KM within complex organizations, as each side of the dichotomy responds to different, and often conflicting, needs: on the one hand, the need to maximize the value of knowledge through its replication; on the other hand, the need to keep knowledge appropriate to an increasingly complex and changing environment. Moreover, as a proposal for a deeper discussion, such trade-off will be suggested as the origin of other relevant KM related trade-offs that will be listed. Managing these trade-offs will be proposed as a main challenge of KM

Languages adapt to their contextual niche

abstractIt is well established that context plays a fundamental role in how we learn and use language. Here we explore how context links short-term language use with the long-term emergence of different types of language system. Using an iterated learning model of cultural transmission, the current study experimentally investigates the role of the communicative situation in which an utterance is produced (situational context) and how it influences the emergence of three types of linguistic systems: underspecified languages (where only some dimensions of meaning are encoded linguistically), holistic systems (lacking systematic structure), and systematic languages (consisting of compound signals encoding both category-level and individuating dimensions of meaning). To do this, we set up a discrimination task in a communication game and manipulated whether the feature dimension shape was relevant or not in discriminating between two referents. The experimental languages gradually evolved to encode information relevant to the task of achieving communicative success, given the situational context in which they are learned and used, resulting in the emergence of different linguistic systems. These results suggest language systems adapt to their contextual niche over iterated learning.</jats:p

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

On two-way communication in cellular automata with a fixed number of cells

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