Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Engineering of Chemical Register MachinesPrague International Workshop on Membrane Computing 2008
R. Fassler, T. Hinze, T. Lenser and P. Dittrich{raf,hinze,thlenser,dittrich}@minet.uni-jena.de
2. June 2008
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Outline
1 MotivationGoalRealizationP-System
2 Register Machines
3 Chemical ImplementationChemical VariablesA Chemical ClockMaster Slave - Flip�opChemical RegistersChemical Program Control
4 Case StudyInteger AdditionMaximum
5 Future Work
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Motivation
Goal: Chemical system with Turing completenessUse mass action kinetics onlyBinary chemical information encodingNo assumptions like molecule structureor a hierarchy of membranes
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Motivation
Realization: Arti�cial chemistry as P-SystemRegisters composed of �ip �ops store informationChemical clock orders operations on registersP-System expands registers if necessary
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
P-Systems as Arti�cial Chemistries
Similarities:
Many autonomous units like molecules or agentsDecentralizationNondeterminismStochasticityData parallelism
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Register Machine
De�nition: M = (R,L, P,#0) withRegisters R = {R1, . . . ,Rm}Labels (addresses) L = {#0, . . . ,#n}Instructions PInitial label #0
Registers store binary values for natural numbers
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
1 MotivationGoalRealizationP-System
2 Register Machines
3 Chemical ImplementationChemical VariablesA Chemical ClockMaster Slave - Flip�opChemical RegistersChemical Program Control
4 Case StudyInteger AdditionMaximum
5 Future Work
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Mass Action Kinetics
De�nition: Speed of an reaction depends on reactantsconcentrations and a constant factorNo saturationNo inhibitors
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Implementation of Logical Variables
Variables: Two species representing "true" and "false"Correlated concentrationsReactions to switch between "true" and "false"Reactions to maintain consistency
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
A Chemical Clock
Based on Belousov- Zhabotinsky reactions
Cascade of variables derives high/low signals
Two o�set oscillators form the clock signal
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Master Slave - Flip�op (MS-FF)
MS-FF: - technical role model
Two-part device storing one bitClocked to switch with o�setShort switches at intended timeOnly one switch per positive edge
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Master Slave - Flip�op
MS-FF: - chemical adaption
Master part switches if triggeredSlave part will adapt master partEncoded by two variablesM/S-reactions separated by two clock signals
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Master Slave - Flip�op
MS-FF: - chemical adaption
Master part switches if triggeredSlave part will adapt master partEncoded by two variablesM/S-reactions separated by two clock signals
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Master Slave - Flip�op
MS-FF: - chemical adaption
Master part switches if triggeredSlave part will adapt master partEncoded by two variablesM/S-reactions separated by two clock signals
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Master Slave - Flip�op
MS-FF: - chemical adaption
Master part switches if triggeredSlave part will adapt master partEncoded by two variablesM/S-reactions separated by two clock signals
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Registers
Registers: One MS-FF for each bit, chainedExtra variable to check if emptyOnly the �rst bit can be �ipped manuallyAdd carries will �ip further bits
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Registers
Registers: One MS-FF for each bit, chainedExtra variable to check if emptyOnly the �rst bit can be �ipped manuallyAdd carries will �ip further bits
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Registers
Registers: One MS-FF for each bit, chainedExtra variable to check if emptyOnly the �rst bit can be �ipped manuallyAdd carries will �ip further bits
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Registers
Registers: One MS-FF for each bit, chainedExtra variable to check if emptyOnly the �rst bit can be �ipped manuallyAdd carries will �ip further bits
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Registers
Registers: One MS-FF for each bit, chainedExtra variable to check if emptyOnly the �rst bit can be �ipped manuallyAdd carries will �ip further bits
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Registers
Registers: One MS-FF for each bit, chainedExtra variable to check if emptyOnly the �rst bit can be �ipped manuallyAdd carries will �ip further bits
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Registers
Registers: One MS-FF for each bit, chainedExtra variable to check if emptyOnly the �rst bit can be �ipped manuallyAdd carries will �ip further bits
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Chemical Program Control
3 Elements per Instruction: #1 : DEC R1 #0
Address - reaction that produces instruction speciesAction - reaction that alters/tests register
Follow up - species encoding the next label
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Case Study
Implemented Examples:
Counter mod 4Integer additionMax(x,y,z)
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Case Study
Integer Addition: 2 + 1 = 3
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Integer Addition
Initialization: 2 + 1 = 3
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Integer Addition
Computation: 2 + 1 = 3
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Maximum of Three Natural Numbers
Computation: max(2, 1, 3)
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Maximum of Three Natural Numbers
Computation: max(2, 1, 3)
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Maximum of Three Natural Numbers
Computation: max(2, 1, 3)
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Maximum of Three Natural Numbers
Computation: max(2, 1, 3)
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Maximum of Three Natural Numbers
Computation: max(2, 1, 3)
Ra�ael Fassler Engineering of Chemical Register Machines
Outline Motivation Register Machines Chemical Implementation Case Study Future Work
Future Work
Parallelization:
Consecutive read/write operations are mergedinto threadsOperations in an thread are performed parallelThreads take the same time as a single operation
Ra�ael Fassler Engineering of Chemical Register Machines