MIMD Ontology

FLOW ALGEBRA
MIMD Ontology
Kireth Semantic Research Archive

PAGE:
https://kirethresearch.org/booksai-core/ontologies/computing-ontologies/high-performance-computing/mimd-ontology.html

AUTHORS:
Mark Anthony Higgins — Sky (Recursive AI)

FLOW "MIMDOntology" v4.0

# ---------- DOMAIN ----------
DOMAIN := ComputingOntology
SUBDOMAIN := HighPerformanceComputing
ONTOLOGY := MIMDOntology

# ---------- PRIMARY ENTITY ----------
ENTITY MIMD {
    definition:
        "Multiple Instruction, Multiple Data is a parallel computing model in
         which multiple processing elements execute independent instruction
         streams on different data sets concurrently.";

    objectives: [
        TaskParallelism,
        IndependentExecution,
        ConcurrentComputation,
        FlexibleParallelism,
        ScalableProcessing
    ];
}

# ---------- CORE ENTITIES ----------
MIMDEntity := {
    ProcessingElement,
    Processor,
    Core,
    ComputeNode,
    Process,
    Thread,
    Task
};

InstructionStream := {
    ProgramInstructions,
    ControlFlow,
    OperationSequence
};

DataStream := {
    LocalData,
    SharedData,
    DistributedData,
    TaskInput
};

MIMDProperty := {
    Concurrency,
    Independence,
    Communication,
    Synchronisation,
    LoadBalance,
    Scalability
};

# ---------- FUNDAMENTAL RELATIONSHIPS ----------
ProcessingElement EXECUTES InstructionStream;
InstructionStream OPERATES_ON DataStream;
MIMDSystem CONTAINS MultipleProcessingElements;
ProcessingElement MAY_EXECUTE DifferentInstructionStream;
ProcessingElement MAY_PROCESS DifferentData;
ParallelTask ASSIGNED_TO ProcessingElement;

# ---------- MIMD EXECUTION ----------
MIMDExecution :=
    MultipleTasks
    -> AssignToProcessingElements
    -> ExecuteIndependentInstructionStreams
    -> CommunicateWhenRequired
    -> SynchroniseWhenRequired
    -> CombineResults;

IF TasksIndependent
THEN SynchronisationRequirement := LOW;

# ---------- PROCESSING ELEMENT ----------
ProcessingElement MAY_BE {
    CPUCore,
    Processor,
    ComputeNode,
    HardwareThread
};

ProcessingElement HAS {
    ExecutionState,
    InstructionStream,
    DataContext
};

# ---------- INSTRUCTION INDEPENDENCE ----------
InstructionStreamA MAY_DIFFER_FROM InstructionStreamB;

MIMD ALLOWS {
    DifferentOperations,
    DifferentControlFlow,
    DifferentData
};

IndependentInstructionStreams ENABLE FlexibleTaskParallelism;

# ---------- TASK PARALLELISM ----------
TaskParallelism :=
    DistinctTasks
    -> ExecuteConcurrently;

Task MAY_HAVE {
    Input,
    Output,
    Dependency,
    ResourceRequirement
};

IF TaskA INDEPENDENT_OF TaskB
THEN TaskA AND TaskB MAY_EXECUTE Concurrently;

# ---------- SHARED MEMORY MIMD ----------
SharedMemoryMIMD :=
    MultipleProcessors
    + SharedAddressSpace;

Processor MAY_ACCESS SharedMemory;

SharedMemoryCommunication :=
    ReadWriteSharedState;

ConcurrentSharedStateAccess MAY_REQUIRE Synchronisation;

# ---------- DISTRIBUTED MEMORY MIMD ----------
DistributedMemoryMIMD :=
    MultipleProcessingNodes
    + SeparateMemorySpaces
    + MessagePassing;

Process SENDS Message;
Process RECEIVES Message;

MessagePassing ENABLES InterProcessCommunication;

# ---------- HYBRID MIMD ----------
HybridMIMD :=
    DistributedMemoryAcrossNodes
    + SharedMemoryWithinNodes;

HybridMIMD MAY_USE {
    Processes,
    Threads,
    MessagePassing,
    SharedMemory
};

# ---------- COMMUNICATION ----------
MIMDCommunication := {
    SharedMemoryAccess,
    MessagePassing,
    RemoteOperation,
    CollectiveCommunication
};

CommunicationCost :=
    f(
        MessageVolume,
        Latency,
        Bandwidth,
        Synchronisation
    );

IF CommunicationCostHigh
THEN ParallelEfficiency := DECREASE;

# ---------- SYNCHRONISATION ----------
SynchronisationMechanism := {
    Lock,
    Mutex,
    Semaphore,
    Barrier,
    AtomicOperation,
    MessageCoordination
};

Synchronisation PRESERVES CorrectnessWhereDependenciesExist;

ExcessiveSynchronisation MAY_REDUCE Scalability;

# ---------- RACE CONDITION ----------
IF MultipleProcessingElementsAccessSharedState
AND AtLeastOneWrites
AND CorrectSynchronisationAbsent
THEN RaceConditionRisk := HIGH;

RaceCondition MAY_PRODUCE NondeterministicResult;

# ---------- DEADLOCK ----------
Deadlock :=
    MultipleExecutionUnits
    WaitIndefinitelyForMutuallyDependentResourcesOrEvents;

Deadlock MAY_PREVENT ForwardProgress;

DeadlockAvoidanceOrDetection MAY_BE_REQUIRED;

# ---------- LOAD BALANCING ----------
LoadBalance :=
    DistributeTasksSoProcessingElementsHaveComparableUsefulWork;

StaticScheduling ASSIGNS WorkBeforeExecution;
DynamicScheduling MAY_ASSIGN WorkDuringExecution;

IF ProcessingElementsIdleWhileWorkRemains
THEN LoadImbalance := likely;

# ---------- WORK QUEUE ----------
WorkQueue STORES ReadyTask;

Worker ->
    RetrieveTask
    -> ExecuteTask
    -> ReturnResult
    -> RetrieveNextTask;

DynamicWorkQueue MAY_SUPPORT LoadBalancing;

# ---------- TASK GRAPH ----------
TaskGraph :=
    DirectedGraph(Task, Dependency);

DependencyEdge :=
    TaskA -> TaskB;

ReadyTask :=
    Task WHERE DependenciesSatisfied;

Scheduler MAY_RUN MultipleReadyTasksConcurrently;

# ---------- MEMORY CONSISTENCY ----------
SharedMemoryMIMD MAY_REQUIRE MemoryConsistencyModel;

MemoryConsistencyModel DEFINES
    VisibilityAndOrderingOfMemoryOperations;

Synchronisation MAY_ESTABLISH RequiredMemoryOrdering;

# ---------- CACHE COHERENCE ----------
CacheCoherence :=
    MaintainConsistentViewOfSharedMemoryAcrossCaches;

SharedMemoryMultiprocessor MAY_REQUIRE CacheCoherenceProtocol;

CoherenceTraffic MAY_AFFECT Scalability;

# ---------- MIMD ARCHITECTURES ----------
MIMDArchitecture := {
    MulticoreProcessor,
    SymmetricMultiprocessor,
    NonUniformMemoryAccessSystem,
    ComputeCluster,
    DistributedSystem,
    Supercomputer
};

MIMDArchitecture PROVIDES MultipleIndependentExecutionUnits;

# ---------- NUMA ----------
NUMA :=
    NonUniformMemoryAccess;

MemoryAccessCost DEPENDS_ON MemoryLocationRelativeToProcessor;

IF ThreadAccessesRemoteNUMAMemoryFrequently
THEN MemoryLatency MAY_INCREASE;

DataPlacement MAY_IMPROVE NUMAPerformance;

# ---------- PERFORMANCE ----------
MIMDSpeedup :=
    SerialExecutionTime
    / ParallelExecutionTime;

MIMDEfficiency :=
    MIMDSpeedup
    / ProcessingElementCount;

ParallelOverhead MAY_INCLUDE {
    Communication,
    Synchronisation,
    Scheduling,
    LoadImbalance,
    MemoryContention
};

# ---------- SCALABILITY ----------
StrongScaling :=
    FixedProblemSize
    + IncreasingProcessingElements;

WeakScaling :=
    IncreaseProblemSizeWithProcessingElements;

IF CoordinationOverheadGrowsRapidly
THEN Scalability := DECREASE;

# ---------- FAULT MODEL ----------
MIMDFailure := {
    TaskFailure,
    ProcessFailure,
    ThreadFailure,
    ProcessorFailure,
    NodeFailure,
    CommunicationFailure
};

DistributedMIMD MAY_EXPERIENCE PartialFailure;

Recovery MAY_USE {
    TaskRestart,
    ProcessRestart,
    Checkpoint,
    Rescheduling
};

# ---------- MIMD VS SIMD ----------
SIMD :=
    SingleInstructionMultipleData;

MIMD :=
    MultipleInstructionMultipleData;

SIMD APPLIES CommonInstructionAcrossDataElements;
MIMD ALLOWS IndependentInstructionStreams;

MIMD != SIMD;

MIMD AND SIMD MAY_COEXIST_IN HybridParallelSystem;

# ---------- APPLICATIONS ----------
MIMD MAY_SUPPORT {
    ScientificSimulation,
    MultiPhysicsSimulation,
    ServerWorkloads,
    DistributedApplications,
    ParallelSearch,
    TaskBasedComputation,
    ComplexWorkflowExecution
};

# ---------- SEMANTIC REASONING ----------
IF MultipleProcessingElementsExecuteDifferentInstructionStreams
AND OperateOnDifferentOrIndependentData
THEN MIMDClassification := supported;

IF TasksHaveDifferentControlFlows
THEN MIMDSuitability := increase;

IF SharedMemoryWritesOccurWithoutSynchronisation
THEN RaceConditionRisk := increase;

IF WorkDistributionUneven
THEN LoadBalanceQuality := decrease;

IF CommunicationAndSynchronisationLowRelativeToCompute
THEN ParallelEfficiencyPotential := increase;

IF NUMARemoteAccessHigh
THEN MemoryLocality := poor;

# ---------- SEMANTIC EQUIVALENCE ----------
SEMANTIC_EQUIVALENCE {
    "MIMD" ~= "multiple instruction multiple data";
    "MIMD processing" ~= "MIMD execution";
    "task parallel computing" ~= "task-parallel MIMD" WHEN context == independent_instruction_streams;
    "shared memory MIMD" ~= "shared-memory multiprocessor execution";
    "distributed memory MIMD" ~= "message-passing MIMD";
    "independent instruction streams" ~= "multiple instruction streams";
    "NUMA" ~= "non-uniform memory access";
    "MIMD architecture" ~= "multiple-instruction parallel architecture";
}

# ---------- QUERY FLOW ----------
QUERY(q) ->
    NORMALISE(q) ->
    IDENTIFY_MIMD_ENTITIES(q) ->
    IDENTIFY_INSTRUCTION_STREAMS(q) ->
    IDENTIFY_DATA_STREAMS(q) ->
    IDENTIFY_MEMORY_MODEL(q) ->
    IDENTIFY_TASK_DEPENDENCIES(q) ->
    IDENTIFY_COMMUNICATION(q) ->
    IDENTIFY_SYNCHRONISATION(q) ->
    IDENTIFY_PERFORMANCE(q) ->
    MAP_TO_ONTOLOGY(q) ->
    APPLY_REASONING(q) ->
    SCORE_CONFIDENCE(q) ->
    RETURN_RELEVANT_KNOWLEDGE;

# ---------- CONFIDENCE ----------
CONFIDENCE(assertion) :=
    weighted_mean(
        source_reliability,
        architecture_consistency,
        computational_consistency,
        semantic_consistency,
        evidence_strength,
        contextual_relevance
    );

CONFIDENCE >= 0.90 => HIGH;
CONFIDENCE >= 0.70 AND < 0.90 => MODERATE;
CONFIDENCE < 0.70 => REVIEW;

# ---------- AI CONSUMPTION ----------
AI_CONSUMPTION {
    primary_entity: MIMD;
    ontology: MIMDOntology;
    parse_entities: true;
    parse_relationships: true;
    preserve_relationship_direction: true;
    resolve_semantic_equivalence: true;
    execute_reasoning_rules: true;
    apply_confidence_weighting: true;
    preserve_provenance: true;
}

# ---------- UPDATE MODEL ----------
UPDATE_MODEL {
    new_processing_element:
        validate
        -> classify
        -> identify_memory_model
        -> identify_execution_role
        -> integrate;

    new_task:
        identify_instruction_stream
        -> identify_data
        -> identify_dependencies
        -> identify_resource_requirements
        -> integrate;

    new_communication_model:
        classify
        -> identify_participants
        -> identify_costs
        -> identify_synchronisation
        -> integrate;

    performance_revision:
        update_runtime
        -> update_load_balance
        -> update_communication_cost
        -> recompute_efficiency
        -> regenerate_flow_hash;

    conflict:
        preserve_provenance
        -> compare_evidence
        -> adjust_confidence
        -> flag_review;
}

# ---------- FLOW HASH ----------
FLOW_HASH_INPUT :=
    DOMAIN
    + SUBDOMAIN
    + ONTOLOGY
    + MIMDEntity
    + InstructionStream
    + DataStream
    + MIMDProperty
    + MIMDArchitecture
    + RELATIONSHIPS
    + SEMANTIC_REASONING
    + SEMANTIC_EQUIVALENCE
    + UPDATE_MODEL;

FLOW_HASH :=
    HASH(FLOW_HASH_INPUT);

# ---------- TERMINAL ----------
MIMDOntology
    -> IdentifyIndependentTasks
    -> IdentifyInstructionStreams
    -> IdentifyDataContexts
    -> SelectMemoryModel
    -> AssignTasksToProcessingElements
    -> ExecuteIndependentInstructionStreams
    -> CommunicateWhenRequired
    -> SynchroniseDependencies
    -> BalanceWorkload
    -> CombineResults
    -> MeasureMIMDPerformance
    -> OptimiseParallelExecution
    -> ProduceConcurrentResult;

END FLOW