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Unlocking the Generative Power of Colonies: Weakly vs. Strongly Competitive Parallel Derivation

Explore the concept of colonies as components in a shared environment, understand weakly and strongly parallel derivation, and delve into the language generated by these systems. Learn about the challenges of blocking wrong words and managing waiting symbols.

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Unlocking the Generative Power of Colonies: Weakly vs. Strongly Competitive Parallel Derivation

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  1. Generative Power of Colonies with Weakly and Strongly Competitive Parallel Derivation Šárka Vavrečková Institute of Computer Science, Silesian University Opava sarka.vavreckova@fpf.slu.cz

  2. Colony – what is it? • Components (agents, very simple robots, etc.). • Shared environment (word, workplace for components). • Timer and number of working components in one moment.

  3. Colony: C = (V, T, R) • V … alphabet of the colony • T … terminal alphabet, T V • R… set of components (S, F), S is notin F The component can work with it: Set of possible results of its work:

  4. Parallel derivation: • Every component which can work, must work. • Each component must be used at most ones (unused symbols = waiting symbols).

  5. Types: • Weakly parallel derivation: if the number of components for some symbol S is bigger then number of S in the environment, we can choose working components. • Strongly parallel derivation: in this case derivation is blocked.

  6. Example: C= (V, T, R), V = {M, N, P, a, b} T = {a, b} R = {(P, {a}), (P, {b}), (N, {M}), (M, {PPPN,PPNP,PNPP,NPPP,})} Axiom w0 = MM

  7. Colony with wp derivation: PPNPM PaMb _ ba _ b bab MM (P, {b}) (N, {M}) (P, {a}) (M, {PPPN,PPNP,PNPP,NPPP,})

  8. Colony with sp derivation: !!! PPNPM PaMb _ MM (P, {b}) (N, {M}) (P, {a}) (M, {PPPN,PPNP,PNPP,NPPP,})

  9. Languages: • L (C, wp, MM) = {w3n; w{a,b}*, |(w,a)–(w,b)|1} • L (C, sp, MM) ={w6n; w{a,b}*,(w,a)=(w,b)} • L (C, CF) = {a,b}3n

  10. Known results: • CF COLwp • CF COLsp COLwp ? COLsp 

  11. Problems: • How to block “wrong words” only(new components must work similarly with the original components). • What shell we do with “waiting symbols” ?

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