Computing with Directed Labeled Graphs

Computing with Directed Labeled Graphs Marko A. Rodriguez Los Alamos National Laboratory Vrije Universiteit Brussel University of California at Santa Cruz [email_address] http://www.soe.ucsc.edu/~okram

Mini-CV. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

My infrastructure. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Main projects. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Digital Library Research and Prototyping Team

The history of this talk. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Outline. ,[object Object],[object Object],[object Object],[object Object]

What is a computer? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The Turing machine. ,[object Object],[object Object],A. M. Turing. On computable numbers, with an application to the entscheidungsproblem. Proceedings of the London Mathematical Society, 42(2):230–265, 1937.

Turing completeness. ,[object Object],[object Object],[object Object],[object Object]

The Von Neumann architecture. ,[object Object],[object Object],[object Object],[object Object],J. von Neumann. The principles of large-scale computing machines. IEEE Annals of the History of Computing, 10(4):243–256, 1988 Processor ( M* ) Data ( D_M ) Instructions ( M ) Memory ( D )

What is in memory? ,[object Object],[object Object],Memory Data: Integer, Float, Memory Address, etc. opcode Instruction: add, subtract, goto 1 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0

What are the types of data? ,[object Object],[object Object],[object Object],[object Object],[object Object],* This is not the standard two’s complement convention. 16 8 4 2 1 * ASCII 7-bit standard for representing characters.

What are the types of instructions? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],A D D 7 43 1 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0

How does a processor compute? ,[object Object],[object Object],Data ( D_M ) Instructions ( M ) Memory ( D ) 0 1 2 3 4 5 6 7 8 9 10 load 7 0 load 8 1 add 0 1 2 store 2 7 goto 0 noop 1..2..3..4..5.. 1 PC Processor ( M* ) 0 1 2 3 registers * Note that memory does not represent characters, just 0 or 1. ALU

Virtual computing machines. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Programming patterns through the ages. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],* Note that all patterns are ultimately represented as lists of instructions in memory.

Object orientation and its relationship to a network. ,[object Object],[object Object],[object Object],marko johan hasFriend hasPaycode $10,000 0000 hasAmount

The undirected network. ,[object Object],[object Object],[object Object],[object Object],[object Object],i j

Example undirected network. Herbert Marko Aric Ed Zhiwu Alberto Jen Johan Luda Stephan Whenzong

The directed network. ,[object Object],[object Object],[object Object],i j

Example directed network. Muskrat Bear Fish Fox Meerkat Lion Human Wolf Deer Beetle Hyena

The semantic network. ,[object Object],[object Object],[object Object],i j s

Example semantic network. SantaFe Marko NewMexico Ryan California UnitedStates LANL livesIn worksWith cityOf originallyFrom stateOf stateOf locatedIn hasLab Cells Atoms madeOf madeOf researches Oregon southOf hasResident Arnold governerOf northOf

Modeling computing data structures with a network. ,[object Object],[object Object],[object Object],[object Object]

A network analog to the Turing model. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],M. A. Rodriguez and J. Bollen. Modeling computations in a semantic network substrate. in review at International Journal of Semantic Computing, LA-UR-07-3678, 2007.

Network representations of the various software patterns. 7 0 load load 8 1 add 0 1 2 store 8 1 someProcedure opA opB opA opA opA opB opB opB opC nextInst nextInst nextInst nextInst 7 0 load load 8 1 add 0 1 2 store 8 1 opA opB opA opA opA opB opB opB opC nextInst nextInst nextInst nextInst 7 0 load load 8 1 add 0 1 2 store 8 1 opA opB opA opA opA opB opB opB opC nextInst nextInst nextInst nextInst someObject hasBody hasBody hasMethod List of Instructions Procedure Object someProcedure

Objects and their relationship to each other and their methods. 7 0 load load 8 1 add 0 1 2 store 8 1 opA opB opA opA opA opB opB opB opC nextInst nextInst nextInst nextInst charges marko hasBody hasMethod 7 0 load load 8 1 add 0 1 2 store 8 1 opA opB opA opA opA opB opB opB opC nextInst nextInst nextInst nextInst addMoney 0000 hasBody hasMethod 7 0 load load 8 1 add 0 1 2 store 8 1 opA opB opA opA opA opB opB opB opC nextInst nextInst nextInst nextInst angry johan hasBody hasFriend hasPaycode hasMethod $10,000 hasAmount * Though not represented, each method should have different instructions.

A virtual machine at its relationship to instructions. PC (current instruction) Method variables LIFO Stack

Physics and its relationship to the virtual machine. M. A. Rodriguez. General-purpose computing on a semantic network substrate. accepted with revisions at Journal of Web Semantics, LA-UR-07-2885, 2007. * Not for the faint of heart. * Ultimately, the only true “computer” is physics. All computing representations must be grounded in physics.

Mapping a semantic network to an undirected network. A computing infrastructure can be represented by dots and lines. M. A. Rodriguez. Mapping Semantic Networks to Undirected Networks. in review at International Journal of Applied Mathematics and Computer Science, LA-UR-07-5287, 2007.

Obviously a network can represent computer instructions and virtual machines. ,[object Object],[object Object],[object Object],[object Object]

A standardized semantic network data model. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],T. Berners-Lee and J. Hendler. Publishing on the Semantic Web. Nature, 410(6832):1023–1024, April 2001.

Triple store technology. SELECT ?a ?c WHERE { ?a type human ?a wrote ?b ?b type article ?c wrote ?b ?c type human ?a != ?c } ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Triple store vs. relational database Triple store Relational Database SQL Interface SPARQL Interface SELECT (?x4) WHERE { ?x1 dc:creator lanl:LAUR-06-2139. ?x1 lanl:hasFriend ?x2 . ?x2 lanl:worksFor ?x3 . ?x3 lanl:collaboratesWith ?x4 . ?x4 lanl:hasEmployee ?x1 . } SELECT collaboratesWithTable.ordId2 FROM personTable, authorTable, articleTable, friendTable, hasEmployeeTable, organizationTable, worksForTable, collaboratesWithTable WHERE personTable.id = authorTable.personId AND authorTable.articleId = "dc:creator LAUR-06-2139" AND personTable.id = friendTable.personId1 AND friendTable.personId2 = worksForTable.personId AND worksForTable.orgId = collaboratesWithTable.orgId2 AND collaboratesWithTable.ordId2 = personTable.id

A distributed semantic network data model. 127.0.0.1 127.0.0.5 127.0.0.2 127.0.0.3 127.0.0.6 127.0.0.4

An RDF program. <http://neno.lanl.gov/instance#42a65d00-71c4-11dc-96bb-000014095701> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://neno.lanl.gov/demo#Example> . <http://neno.lanl.gov/instance#42a65d00-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#hasMethod> <http://neno.lanl.gov/instance#42a65d01-71c4-11dc-96bb-000014095701> . <http://neno.lanl.gov/instance#42a65d01-71c4-11dc-96bb-000014095701> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://neno.lanl.gov/demo#130ec6a7-8f0a-4f49-adec-b399c849bb9b> . <http://neno.lanl.gov/instance#42a65d01-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#hasArgumentDescriptor> <http://neno.lanl.gov/instance#42a65d03-71c4-11dc-96bb-000014095701> . <http://neno.lanl.gov/instance#42a65d03-71c4-11dc-96bb-000014095701> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://neno.lanl.gov#ArgumentDescriptor> . <http://neno.lanl.gov/instance#42a65d03-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#_a0> <http://neno.lanl.gov/instance#42a65d02-71c4-11dc-96bb-000014095701> . <http://neno.lanl.gov/instance#42a65d02-71c4-11dc-96bb-000014095701> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://neno.lanl.gov#Argument> . <http://neno.lanl.gov/instance#42a65d02-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#hasSymbol> "n"^^<http://www.w3.org/2001/XMLSchema#string> . <http://neno.lanl.gov/instance#42a65d02-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#hasType> "http://www.w3.org/2001/XMLSchema#integer . <http://neno.lanl.gov/instance#42a65d01-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#hasMethodName> "test"^^<http://www.w3.org/2001/XMLSchema#string> . <http://neno.lanl.gov/instance#42a65d01-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#hasBlock> <http://neno.lanl.gov/instance#42a65d04-71c4-11dc-96bb-000014095701> . <http://neno.lanl.gov/instance#42a65d04-71c4-11dc-96bb-000014095701> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://neno.lanl.gov#Block> . <http://neno.lanl.gov/instance#42a65d04-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#nextInst> <http://neno.lanl.gov/instance#42a65d05-71c4-11dc-96bb-000014095701> . <http://neno.lanl.gov/instance#42a65d05-71c4-11dc-96bb-000014095701> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://neno.lanl.gov#Set> . <http://neno.lanl.gov/instance#42a65d05-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#hasLeft> <http://neno.lanl.gov/instance#42a65d06-71c4-11dc-96bb-000014095701> . <http://neno.lanl.gov/instance#42a65d06-71c4-11dc-96bb-000014095701> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://neno.lanl.gov#LocalVariable> . <http://neno.lanl.gov/instance#42a65d06-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#hasSymbol> "n"^^<http://www.w3.org/2001/XMLSchema#string> . <http://neno.lanl.gov/instance#42a65d05-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#hasRight> <http://neno.lanl.gov/instance#42a65d07-71c4-11dc-96bb-000014095701> . <http://neno.lanl.gov/instance#42a65d07-71c4-11dc-96bb-000014095701> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://neno.lanl.gov#PopLiteral> . <http://neno.lanl.gov/instance#42a65d05-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#nextInst> <http://neno.lanl.gov/instance#42a65d08-71c4-11dc-96bb-000014095701> . <http://neno.lanl.gov/instance#42a65d08-71c4-11dc-96bb-000014095701> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://neno.lanl.gov#Block> . <http://neno.lanl.gov/instance#42a65d08-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#nextInst> <http://neno.lanl.gov/instance#42a65d09-71c4-11dc-96bb-000014095701> . <http://neno.lanl.gov/instance#42a65d09-71c4-11dc-96bb-000014095701> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://neno.lanl.gov#PushValue> . <http://neno.lanl.gov/instance#42a65d09-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#hasValue> <http://neno.lanl.gov/instance#42a65d0a-71c4-11dc-96bb-000014095701> . <http://neno.lanl.gov/instance#42a65d0a-71c4-11dc-96bb-000014095701> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://neno.lanl.gov#LocalDirect> . <http://neno.lanl.gov/instance#42a65d0a-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#hasURI> "0"^^<http://www.w3.org/2001/XMLSchema#integer> . <http://neno.lanl.gov/instance#42a65d09-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#nextInst> <http://neno.lanl.gov/instance#42a65d0b-71c4-11dc-96bb-000014095701> . <http://neno.lanl.gov/instance#42a65d0b-71c4-11dc-96bb-000014095701> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://neno.lanl.gov#Set> . <http://neno.lanl.gov/instance#42a65d0b-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#hasLeft> <http://neno.lanl.gov/instance#42a65d0c-71c4-11dc-96bb-000014095701> . <http://neno.lanl.gov/instance#42a65d0c-71c4-11dc-96bb-000014095701> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://neno.lanl.gov#LocalVariable> . <http://neno.lanl.gov/instance#42a65d0c-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#hasSymbol> "i"^^<http://www.w3.org/2001/XMLSchema#string> . <http://neno.lanl.gov/instance#42a65d0b-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#hasRight> <http://neno.lanl.gov/instance#42a65d0d-71c4-11dc-96bb-000014095701> . <http://neno.lanl.gov/instance#42a65d0d-71c4-11dc-96bb-000014095701> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://neno.lanl.gov#PopLiteral> . <http://neno.lanl.gov/instance#42a65d0b-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#nextInst> <http://neno.lanl.gov/instance#42a65d0e-71c4-11dc-96bb-000014095701> . <http://neno.lanl.gov/instance#42a65d0e-71c4-11dc-96bb-000014095701> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://neno.lanl.gov#LessThan> . <http://neno.lanl.gov/instance#42a65d0e-71c4-11dc-96bb-000014095701> <http://neno.lanl.gov#hasLeft> <http://neno.lanl.gov/instance#42a65d0f-71c4-11dc-96bb-000014095701> . … .. .

Open computing. ,[object Object],[object Object],[object Object],[object Object],M. A. Rodriguez and J. Shinavier. The RDF Virtual Machine. in review at 2008 World Wide Web Conference, Beijing, China, 2007.

Distributed computing. ,[object Object],[object Object],R/T : Virtual Machine and Stored Program D? : Data

Reflective computing. ,[object Object],[object Object],[object Object],[object Object]

A new level of abstraction. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Future research objectives. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],V. B. Mountcastle. An organizing principle for cerebral function: the unit model and the distributed system. In G. Edelman and V. Mountcastle, editors, Mindful Brain: Cortical Organization and the Group-Selective Theory of Higher Brain Function. MIT Press, Cambridge, Mass., 1978.

Computing with Directed Labeled Graphs

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