Towards Context-Based Concurrent Formal Theories

Schumann, Andrew

doi:10.1142/s0129626415400083

Cited by 22 publications

(16 citation statements)

References 5 publications

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“…The amoeboid reactions with the n inputs and the m > n outputs can be considered a hybrid action [20]. The set of hybrid actions can have an infinite set of labels [20].…”

Section: Undecidable Functions In Actin Filament Networkmentioning

confidence: 99%

On Arithmetic Functions in Actin Filament Networks

Schumann¹

2017

Proceedings of the 10th EAI International Conference on Bio-Inspired Information and Communications Technologies (Formerly BION

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This paper is devoted to actin filament networks as a computation medium. The point is that actin filaments are sensitive to outer cellular stimuli (attractants as well as repellents) and they appear and disappear at different places of the cell to change the cell structure, e.g. its shape. Due to assembling and disassembling actin filaments, Amoeba proteus can move in responses to different stimuli. As a result, Amoeba proteus can be considered a simple reversible logic gate, where outer cellular signals are its inputs and the amoeba motions are its outputs. In this way, we can implement the FREDKIN logic gate on the amoeba behaviours. The actin filament networks have the same basic properties as neural networks: lateral inhibition; lateral activation; recurrent inhibition; recurrent excitation; feedforward inhibition; feedforward excitation; convergence/divergence. These networks can embody arithmetic functions defined recursively and corecursively within p-adic valued logic. Furthermore, within these networks we can define the so-called diagonalization for deducing undecidable arithmetic functions.

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“…The amoeboid reactions with the n inputs and the m > n outputs can be considered a hybrid action [20]. The set of hybrid actions can have an infinite set of labels [20].…”

Section: Undecidable Functions In Actin Filament Networkmentioning

confidence: 99%

On Arithmetic Functions in Actin Filament Networks

Schumann¹

2017

Proceedings of the 10th EAI International Conference on Bio-Inspired Information and Communications Technologies (Formerly BION

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“…The point is that under these conditions we cannot approximate elementary (atomic) acts, i.e. we deal with a massive-parallel behaviour of plasmodia (they are to be expanded in all possible directions) [6], [17], [20]. Hence, we must extend our OPL-Ph by some unconventional tools to make OPL-Ph applicable for the case of nutrient-rich substrate, also.…”

Section: 1non-aristotelian Extensions Of Storage Modification Machmentioning

confidence: 99%

“…We have constructed an unconventional logic, which deals with non-well-founded data, namely with infinite streams and wave sets (sets of mutually defined infinite streams) [8], [17], [30]. Within this logic we can logically combine cellular automata, where Boolean functions are regarded as local transition rules which can change at in time.…”

Section: 2reflexive Gamesmentioning

confidence: 99%

“…Taking into account the fact that the plasmodium is very sensitive to the environment and can change its strategies we can extent the standard notion of cellular automata and assume that transition rules can change in an appropriate neighbourhood in accordance with some outer conditions at time step t = 0, 1, 2... The theory of these automata with changing transition rules is proposed in [8], [17].…”

Section: 3cellular Automatamentioning

confidence: 99%

“…The plasmodium implements cellular automata with changing transition rules. Within these automata we can define context-based concurrent formal theories [5], [14], [17].…”

Section: 3cellular Automatamentioning

confidence: 99%

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Logics for Physarum Chips

Schumann

Pancerz

2016

Studia Humana

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The paper considers main features of two groups of logics for biological devices, called Physarum Chips, based on the plasmodium. Let us recall that the plasmodium is a single cell with many diploid nuclei. It propagates networks by growing pseudopodia to connect scattered nutrients (pieces of food). As a result, we deal with a kind of computing. The first group of logics for Physarum Chips formalizes the plasmodium behaviour under conditions of nutrient-poor substrate. This group can be defined as standard storage modification machines. The second group of logics for Physarum Chips covers the plasmodium computing under conditions of nutrient-rich substrate. In this case the plasmodium behaves in a massively parallel manner and propagates in all possible directions. The logics of the second group are unconventional and deal with non-well-founded data such as infinite streams.

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Conventional and Unconventional Approaches to Swarm Logic

Schumann

2016

Emergence, Complexity and Computation

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Towards Context-Based Concurrent Formal Theories

Cited by 22 publications

References 5 publications

On Arithmetic Functions in Actin Filament Networks

On Arithmetic Functions in Actin Filament Networks

Logics for Physarum Chips

Conventional and Unconventional Approaches to Swarm Logic

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