Engineering of Chemical Register Machines

Transkript

1 Prague International Workshop on Membrane Computing 2008 R. Fassler, T. Hinze, T. Lenser and P. Dittrich 2. June 2008

2 Outline 1 Motivation Goal Realization P-System 2 Register Machines 3 Chemical Implementation Chemical Variables A Chemical Clock Master Slave - Flipop Chemical Registers Chemical Program Control 4 Case Study Integer Addition Maximum 5 Future Work

3 Motivation Goal: Chemical system with Turing completeness Use mass action kinetics only Binary chemical information encoding No assumptions like molecule structure or a hierarchy of membranes

4 Motivation Realization: Articial chemistry as P-System Registers composed of ip ops store information Chemical clock orders operations on registers P-System expands registers if necessary

5 P-Systems as Articial Chemistries Similarities: Many autonomous units like molecules or agents Decentralization Nondeterminism Stochasticity Data parallelism

6 Register Machine Denition: M = (R, L, P, # 0 ) with Registers R = {R 1,..., R m } Labels (addresses) L = {# 0,..., # n } Instructions P Initial label # 0 Registers store binary values for natural numbers

7 1 Motivation Goal Realization P-System 2 Register Machines 3 Chemical Implementation Chemical Variables A Chemical Clock Master Slave - Flipop Chemical Registers Chemical Program Control 4 Case Study Integer Addition Maximum 5 Future Work

8 Mass Action Kinetics Denition: Speed of an reaction depends on reactants concentrations and a constant factor No saturation No inhibitors

9 Chemical Implementation of Logical Variables Variables: Two species representing "true" and "false" Correlated concentrations Reactions to switch between "true" and "false" Reactions to maintain consistency

10 A Chemical Clock Based on Belousov- Zhabotinsky reactions Cascade of variables derives high/low signals Two oset oscillators form the clock signal

11 Master Slave - Flipop (MS-FF) MS-FF: - technical role model Two-part device storing one bit Clocked to switch with oset Short switches at intended time Only one switch per positive edge

12 Master Slave - Flipop MS-FF: - chemical adaption Master part switches if triggered Slave part will adapt master part Encoded by two variables M/S-reactions separated by two clock signals

13 Master Slave - Flipop MS-FF: - chemical adaption Master part switches if triggered Slave part will adapt master part Encoded by two variables M/S-reactions separated by two clock signals

14 Master Slave - Flipop MS-FF: - chemical adaption Master part switches if triggered Slave part will adapt master part Encoded by two variables M/S-reactions separated by two clock signals

15 Master Slave - Flipop MS-FF: - chemical adaption Master part switches if triggered Slave part will adapt master part Encoded by two variables M/S-reactions separated by two clock signals

16 Chemical Registers Registers: One MS-FF for each bit, chained Extra variable to check if empty Only the rst bit can be ipped manually Add carries will ip further bits

17 Chemical Registers Registers: One MS-FF for each bit, chained Extra variable to check if empty Only the rst bit can be ipped manually Add carries will ip further bits

18 Chemical Registers Registers: One MS-FF for each bit, chained Extra variable to check if empty Only the rst bit can be ipped manually Add carries will ip further bits

19 Chemical Registers Registers: One MS-FF for each bit, chained Extra variable to check if empty Only the rst bit can be ipped manually Add carries will ip further bits

20 Chemical Registers Registers: One MS-FF for each bit, chained Extra variable to check if empty Only the rst bit can be ipped manually Add carries will ip further bits

21 Chemical Registers Registers: One MS-FF for each bit, chained Extra variable to check if empty Only the rst bit can be ipped manually Add carries will ip further bits

22 Chemical Registers Registers: One MS-FF for each bit, chained Extra variable to check if empty Only the rst bit can be ipped manually Add carries will ip further bits

23 Chemical Program Control 3 Elements per Instruction: # 1 : DEC R 1 # 0 Address - reaction that produces instruction species Action - reaction that alters/tests register Follow up - species encoding the next label

24 Chemical Program Control 3 Elements per Instruction: # 1 : DEC R 1 # 0 Address - reaction that produces instruction species Action - reaction that alters/tests register Follow up - species encoding the next label

25 Chemical Program Control 3 Elements per Instruction: # 1 : DEC R 1 # 0 Address - reaction that produces instruction species Action - reaction that alters/tests register Follow up - species encoding the next label

26 Chemical Program Control 3 Elements per Instruction: # 1 : DEC R 1 # 0 Address - reaction that produces instruction species Action - reaction that alters/tests register Follow up - species encoding the next label

27 Chemical Program Control 3 Elements per Instruction: # 1 : DEC R 1 # 0 Address - reaction that produces instruction species Action - reaction that alters/tests register Follow up - species encoding the next label

28 Chemical Program Control 3 Elements per Instruction: # 1 : DEC R 1 # 0 Address - reaction that produces instruction species Action - reaction that alters/tests register Follow up - species encoding the next label

29 Chemical Program Control 3 Elements per Instruction: # 1 : DEC R 1 # 0 Address - reaction that produces instruction species Action - reaction that alters/tests register Follow up - species encoding the next label

30 Chemical Program Control 3 Elements per Instruction: # 1 : DEC R 1 # 0 Address - reaction that produces instruction species Action - reaction that alters/tests register Follow up - species encoding the next label

31 Chemical Program Control 3 Elements per Instruction: # 1 : DEC R 1 # 0 Address - reaction that produces instruction species Action - reaction that alters/tests register Follow up - species encoding the next label

32 Case Study Implemented Examples: Counter mod 4 Integer addition Max(x,y,z)

33 Case Study Integer Addition: = 3

34 Integer Addition Initialization: = 3

35 Integer Addition Computation: = 3

36 Maximum of Three Natural Numbers Computation: max(2, 1, 3)

37 Maximum of Three Natural Numbers Computation: max(2, 1, 3)

38 Maximum of Three Natural Numbers Computation: max(2, 1, 3)

39 Maximum of Three Natural Numbers Computation: max(2, 1, 3)

40 Maximum of Three Natural Numbers Computation: max(2, 1, 3)

41 Future Work Parallelization: Consecutive read/write operations are merged into threads Operations in an thread are performed parallel Threads take the same time as a single operation

42 Thank you for your attention!