@sschepis/resolang/assembly/examples/turing-machine-simulator.ts

ResoLang - Core quantum resonance computation library for browser and Node.js

/**
 * Quantum-Enhanced Turing Machine Simulator for P ≠ NP Proof
 * 
 * This module implements a Turing machine simulator with quantum-inspired features
 * for tracking self-referential complexity. It integrates with the Gödel encoding
 * system and self-referential complexity tracker to demonstrate the key concepts
 * in Muñoz de la Cuesta's P ≠ NP proof.
 * 
 * The simulator tracks every computational step and identifies self-referential
 * operations where the machine accesses its own description or prior configurations.
 */

import { 
  ResonantFragment, 
  EntangledNode,
  Prime
} from '../resolang';
import {
  tensor,
  entropy,
  collapse
} from '../operators';
import { toFixed } from '../utils';
import { 
  SelfReferentialTracker, 
  ComputationStep,
  VerificationResult,
  ComplexityAnalysis 
} from './self-referential-complexity';
import {
  TuringConfiguration,
  TuringMachineEncoder,
  Transition,
  QuantumGodelEncoder,
  GodelComplexityReport
} from './godel-encoding';

// ============================================================================
// TURING MACHINE CORE COMPONENTS
// ============================================================================

/**
 * Tape representation with infinite (expandable) memory
 */
export class TuringTape {
  private cells: Array<string>;
  private headPosition: i32;
  private blankSymbol: string;
  
  constructor(initialContent: string = "", blankSymbol: string = "B") {
    this.cells = new Array<string>();
    this.blankSymbol = blankSymbol;
    this.headPosition = 0;
    
    // Initialize tape with content
    if (initialContent.length > 0) {
      for (let i = 0; i < initialContent.length; i++) {
        this.cells.push(initialContent.charAt(i));
      }
    } else {
      this.cells.push(this.blankSymbol);
    }
  }
  
  /**
   * Read symbol at current head position
   */
  public read(): string {
    this.ensureCapacity();
    return this.cells[this.headPosition];
  }
  
  /**
   * Write symbol at current head position
   */
  public write(symbol: string): void {
    this.ensureCapacity();
    this.cells[this.headPosition] = symbol;
  }
  
  /**
   * Move head left or right
   */
  public moveHead(direction: string): void {
    if (direction === "L") {
      this.headPosition = Math.max(0, this.headPosition - 1);
    } else if (direction === "R") {
      this.headPosition++;
    }
    this.ensureCapacity();
  }
  
  /**
   * Get current head position
   */
  public getHeadPosition(): i32 {
    return this.headPosition;
  }
  
  /**
   * Get tape content as string (visible portion)
   */
  public getContent(): string {
    let content = "";
    for (let i = 0; i < this.cells.length; i++) {
      if (this.cells[i] !== this.blankSymbol || i <= this.headPosition + 2) {
        content += this.cells[i];
      }
    }
    return content.length > 0 ? content : this.blankSymbol;
  }
  
  /**
   * Ensure tape has sufficient capacity
   */
  private ensureCapacity(): void {
    while (this.headPosition >= this.cells.length) {
      this.cells.push(this.blankSymbol);
    }
  }
  
  /**
   * Create quantum representation of tape state
   */
  public toQuantumState(): ResonantFragment {
    const tapeContent = this.getContent();
    const positionEncoding = `pos_${this.headPosition}`;
    const combined = `${tapeContent}_${positionEncoding}`;
    return ResonantFragment.encode(combined);
  }
}

/**
 * Quantum-enhanced Turing machine state
 */
export class QuantumTuringMachine {
  private machine: TuringMachineEncoder;
  private tape: TuringTape;
  private currentState: string;
  private stepCount: i32;
  private maxSteps: i32;
  
  // Quantum and complexity tracking
  private complexityTracker: SelfReferentialTracker;
  private godelEncoder: QuantumGodelEncoder;
  private quantumStates: Array<ResonantFragment>;
  private stateHistory: Array<string>;
  
  // Computation results
  private halted: bool;
  private accepted: bool;
  
  constructor(
    machine: TuringMachineEncoder,
    input: string,
    maxSteps: i32 = 1000
  ) {
    this.machine = machine;
    this.tape = new TuringTape(input);
    this.currentState = machine.startState;
    this.stepCount = 0;
    this.maxSteps = maxSteps;
    this.halted = false;
    this.accepted = false;
    
    // Initialize tracking systems
    this.complexityTracker = new SelfReferentialTracker(machine.toString());
    this.godelEncoder = new QuantumGodelEncoder(machine);
    this.quantumStates = new Array<ResonantFragment>();
    this.stateHistory = new Array<string>();
    
    // Record initial configuration
    this.recordCurrentConfiguration();
  }
  
  /**
   * Execute a single step of the Turing machine
   */
  public step(): bool {
    if (this.halted || this.stepCount >= this.maxSteps) {
      return false;
    }
    
    // Read current tape symbol
    const currentSymbol = this.tape.read();
    
    // Find applicable transition
    const transition = this.findTransition(this.currentState, currentSymbol);
    
    if (!transition) {
      // No transition found - halt and reject
      this.halted = true;
      this.accepted = false;
      return false;
    }
    
    // Execute transition
    this.tape.write(transition.writeSymbol);
    this.tape.moveHead(transition.direction);
    
    // Update state
    const previousState = this.currentState;
    this.currentState = transition.toState;
    this.stepCount++;
    
    // Record configuration and check for self-reference
    this.recordCurrentConfiguration();
    this.checkSelfreferentialAccess(transition, previousState);
    
    // Check for acceptance
    if (this.isAcceptState(this.currentState)) {
      this.halted = true;
      this.accepted = true;
    }
    
    return true;
  }
  
  /**
   * Run the machine until halt or max steps
   */
  public run(): MachineResult {
    const startTime = Date.now();
    
    while (this.step()) {
      // Continue until halt or max steps
    }
    
    const totalTime = Date.now() - startTime;
    
    // Generate comprehensive results
    return this.generateResult(totalTime);
  }
  
  /**
   * Find transition for current state and symbol
   */
  private findTransition(state: string, symbol: string): Transition | null {
    for (let i = 0; i < this.machine.transitions.length; i++) {
      const t = this.machine.transitions[i];
      if (t.fromState === state && t.readSymbol === symbol) {
        return t;
      }
    }
    return null;
  }
  
  /**
   * Check if state is an accept state
   */
  private isAcceptState(state: string): bool {
    for (let i = 0; i < this.machine.acceptStates.length; i++) {
      if (this.machine.acceptStates[i] === state) {
        return true;
      }
    }
    return false;
  }
  
  /**
   * Record current configuration for complexity analysis
   */
  private recordCurrentConfiguration(): void {
    // Create Turing configuration
    const config = new TuringConfiguration(
      this.currentState,
      this.tape.getContent(),
      this.tape.getHeadPosition(),
      this.stepCount
    );
    
    // Add to Gödel encoder
    this.godelEncoder.addConfiguration(config);
    
    // Create computation step for complexity tracker
    const transitionDesc = `step_${this.stepCount}_${this.currentState}`;
    const step = new ComputationStep(
      this.stepCount,
      this.currentState,
      this.tape.getHeadPosition(),
      this.tape.getContent(),
      transitionDesc
    );
    
    this.complexityTracker.addStep(step);
    
    // Store quantum state
    const quantumState = this.tape.toQuantumState();
    this.quantumStates.push(quantumState);
    this.stateHistory.push(this.currentState);
  }
  
  /**
   * Check for self-referential access in current step
   */
  private checkSelfreferentialAccess(transition: Transition, previousState: string): void {
    // Check if transition involves state introspection
    if (this.isIntrospectiveTransition(transition)) {
      console.log(`[SELF-REF] Step ${this.stepCount}: Introspective transition detected`);
    }
    
    // Check if returning to previous state (self-referential)
    if (transition.toState === previousState) {
      console.log(`[SELF-REF] Step ${this.stepCount}: State loop detected - returning to ${previousState}`);
    }
    
    // Check if accessing prior tape configurations
    for (let i = 0; i < this.stepCount - 1; i++) {
      if (this.godelEncoder.isSelfreferentialAccess(this.stepCount, i)) {
        console.log(`[SELF-REF] Step ${this.stepCount}: Accessing prior configuration from step ${i}`);
      }
    }
  }
  
  /**
   * Check if transition involves machine introspection
   */
  private isIntrospectiveTransition(transition: Transition): bool {
    // Check for introspective patterns in state names
    const introspectiveKeywords = ["check", "verify", "loop", "return", "compare"];
    
    for (let i = 0; i < introspectiveKeywords.length; i++) {
      if (transition.toState.includes(introspectiveKeywords[i]) || 
          transition.fromState.includes(introspectiveKeywords[i])) {
        return true;
      }
    }
    
    return false;
  }
  
  /**
   * Generate comprehensive machine result
   */
  private generateResult(executionTime: i32): MachineResult {
    const complexityAnalysis = this.complexityTracker.getComplexityAnalysis();
    const godelReport = this.godelEncoder.getComplexityReport();
    const fundamentalLemma = this.complexityTracker.verifyFundamentalLemma(executionTime);
    
    return new MachineResult(
      this.accepted,
      this.halted,
      this.stepCount,
      executionTime,
      this.tape.getContent(),
      complexityAnalysis,
      godelReport,
      fundamentalLemma,
      this.quantumStates
    );
  }
  
  /**
   * Get current machine status
   */
  public getStatus(): string {
    return `State: ${this.currentState}, Steps: ${this.stepCount}, Halted: ${this.halted}, Accepted: ${this.accepted}`;
  }
}

/**
 * Comprehensive machine execution result
 */
export class MachineResult {
  public accepted: bool;
  public halted: bool;
  public totalSteps: i32;
  public executionTime: i32;
  public finalTapeContent: string;
  public complexityAnalysis: ComplexityAnalysis;
  public godelReport: GodelComplexityReport;
  public fundamentalLemmaVerification: VerificationResult;
  public quantumStates: Array<ResonantFragment>;
  
  constructor(
    accepted: bool,
    halted: bool,
    totalSteps: i32,
    executionTime: i32,
    finalTapeContent: string,
    complexityAnalysis: ComplexityAnalysis,
    godelReport: GodelComplexityReport,
    fundamentalLemmaVerification: VerificationResult,
    quantumStates: Array<ResonantFragment>
  ) {
    this.accepted = accepted;
    this.halted = halted;
    this.totalSteps = totalSteps;
    this.executionTime = executionTime;
    this.finalTapeContent = finalTapeContent;
    this.complexityAnalysis = complexityAnalysis;
    this.godelReport = godelReport;
    this.fundamentalLemmaVerification = fundamentalLemmaVerification;
    this.quantumStates = quantumStates;
  }
  
  /**
   * Calculate self-referential complexity ratio
   */
  public getSelfreferentialRatio(): f64 {
    return this.complexityAnalysis.ratio;
  }
  
  /**
   * Check if computation demonstrates exponential self-referential growth
   */
  public hasExponentialComplexity(): bool {
    return this.complexityAnalysis.classification === "HIGH" || 
           this.complexityAnalysis.classification === "EXTREME";
  }
  
  public toString(): string {
    return `MachineResult(accepted=${this.accepted}, steps=${this.totalSteps}, ` +
           `complexity_ratio=${toFixed(this.getSelfreferentialRatio(), 3)}, ` +
           `classification=${this.complexityAnalysis.classification})`;
  }
}

// ============================================================================
// SPECIALIZED MACHINES FOR P ≠ NP DEMONSTRATION
// ============================================================================

/**
 * Factory for creating machines that demonstrate self-referential complexity
 */
export class PvsNPMachineFactory {
  
  /**
   * Create a simple machine with self-referential behavior
   */
  public static createSelfreferentialMachine(): TuringMachineEncoder {
    const states = ["q0", "q1", "q_check", "q_loop", "qaccept", "qreject"];
    const alphabet = ["0", "1", "B"];
    
    const transitions = [
      // Normal computation
      new Transition("q0", "0", "q1", "1", "R"),
      new Transition("q0", "1", "q_check", "0", "L"), // Enter self-referential phase
      
      // Self-referential checking phase
      new Transition("q_check", "1", "q_loop", "1", "L"), // Check prior state
      new Transition("q_check", "0", "q0", "0", "R"),     // Return to q0 (self-referential!)
      
      // Loop detection (highly self-referential)
      new Transition("q_loop", "0", "q_check", "0", "R"), // Loop back to check
      new Transition("q_loop", "1", "qaccept", "1", "R"), // Accept
      new Transition("q_loop", "B", "qreject", "B", "R")  // Reject
    ];
    
    return new TuringMachineEncoder(states, alphabet, transitions, "q0", ["qaccept"]);
  }
  
  /**
   * Create a machine that simulates binary search behavior (for SAT demonstration)
   */
  public static createBinarySearchMachine(): TuringMachineEncoder {
    const states = ["q_start", "q_search", "q_verify", "q_left", "q_right", "qaccept", "qreject"];
    const alphabet = ["0", "1", "X", "B"];
    
    const transitions = [
      // Start phase
      new Transition("q_start", "0", "q_search", "X", "R"),
      new Transition("q_start", "1", "q_search", "X", "R"),
      new Transition("q_start", "B", "qaccept", "B", "R"),
      
      // Search phase (self-referential - checks previously marked positions)
      new Transition("q_search", "0", "q_verify", "0", "L"), // Verify previous choices
      new Transition("q_search", "1", "q_verify", "1", "L"), // Verify previous choices
      new Transition("q_search", "X", "q_left", "X", "R"),   // Skip marked, go left
      
      // Verification (highly self-referential)
      new Transition("q_verify", "X", "q_search", "X", "R"), // Return to search
      new Transition("q_verify", "0", "q_right", "0", "R"),  // Go right branch
      new Transition("q_verify", "1", "q_left", "1", "R"),   // Go left branch
      
      // Branch exploration
      new Transition("q_left", "0", "q_verify", "X", "L"),   // Mark and verify
      new Transition("q_left", "1", "qreject", "1", "R"),    // Conflict
      new Transition("q_right", "1", "q_verify", "X", "L"),  // Mark and verify
      new Transition("q_right", "0", "qreject", "0", "R"),   // Conflict
      new Transition("q_right", "B", "qaccept", "B", "R")    // Success
    ];
    
    return new TuringMachineEncoder(states, alphabet, transitions, "q_start", ["qaccept"]);
  }
  
  /**
   * Create a machine that demonstrates exponential self-referential complexity
   */
  public static createExponentialComplexityMachine(): TuringMachineEncoder {
    const states = ["q0", "q1", "q2", "q_double", "q_verify_all", "qaccept"];
    const alphabet = ["0", "1", "B"];
    
    // This machine doubles its verification work at each step
    const transitions = [
      new Transition("q0", "0", "q1", "1", "R"),
      new Transition("q0", "1", "q_double", "0", "L"),
      
      // Doubling phase - each step requires checking all previous steps
      new Transition("q_double", "0", "q_verify_all", "0", "L"), // Verify ALL previous
      new Transition("q_double", "1", "q_verify_all", "1", "L"), // Verify ALL previous
      
      // Verification requires checking every prior configuration
      new Transition("q_verify_all", "0", "q1", "0", "R"),       // Check against q1
      new Transition("q_verify_all", "1", "q2", "1", "R"),       // Check against q2
      new Transition("q_verify_all", "B", "q0", "B", "R"),       // Back to start
      
      // Secondary states for verification
      new Transition("q1", "0", "q2", "1", "R"),
      new Transition("q1", "1", "q_verify_all", "0", "L"),       // Recursive verification
      new Transition("q2", "0", "qaccept", "0", "R"),
      new Transition("q2", "1", "q_verify_all", "1", "L")        // Recursive verification
    ];
    
    return new TuringMachineEncoder(states, alphabet, transitions, "q0", ["qaccept"]);
  }
}

// ============================================================================
// EXAMPLE DEMONSTRATIONS
// ============================================================================

/**
 * Example 1: Basic Turing Machine Operation
 */
export function demonstrateBasicTuringMachine(): void {
  console.log("=== Example 1: Basic Turing Machine Operation ===");
  
  const machine = PvsNPMachineFactory.createSelfreferentialMachine();
  const tm = new QuantumTuringMachine(machine, "010", 50);
  
  console.log("Initial status: " + tm.getStatus());
  
  // Run a few steps manually
  for (let i = 0; i < 5 && tm.step(); i++) {
    console.log(`Step ${i + 1}: ${tm.getStatus()}`);
  }
  
  // Complete the run
  const result = tm.run();
  console.log(`Final result: ${result.toString()}`);
  console.log(`Fundamental lemma verified: ${result.fundamentalLemmaVerification.verified}`);
}

/**
 * Example 2: Binary Search Machine Simulation
 */
export function demonstrateBinarySearchMachine(): void {
  console.log("\n=== Example 2: Binary Search Machine ===");
  
  const machine = PvsNPMachineFactory.createBinarySearchMachine();
  const tm = new QuantumTuringMachine(machine, "0110", 100);
  
  const result = tm.run();
  
  console.log(`Binary search result: ${result.toString()}`);
  console.log(`Self-referential complexity: ${result.complexityAnalysis.selfreferentialSteps}/${result.totalSteps}`);
  console.log(`Complexity classification: ${result.complexityAnalysis.classification}`);
  console.log(`Has exponential complexity: ${result.hasExponentialComplexity()}`);
}

/**
 * Example 3: Exponential Complexity Demonstration
 */
export function demonstrateExponentialComplexity(): void {
  console.log("\n=== Example 3: Exponential Complexity Machine ===");
  
  const machine = PvsNPMachineFactory.createExponentialComplexityMachine();
  const tm = new QuantumTuringMachine(machine, "01", 200);
  
  const result = tm.run();
  
  console.log(`Exponential machine result: ${result.toString()}`);
  console.log(`Gödel report: ${result.godelReport.toString()}`);
  console.log(`Fundamental lemma constant: ${toFixed(result.fundamentalLemmaVerification.constant, 3)}`);
  
  // Show complexity growth pattern
  console.log("Complexity growth pattern:");
  for (let i = 0; i < Math.min(result.complexityAnalysis.growthPattern.length, 10); i++) {
    console.log(`  Step ${i}: ${result.complexityAnalysis.growthPattern[i]} cumulative self-ref steps`);
  }
}

/**
 * Example 4: Quantum State Evolution
 */
export function demonstrateQuantumStateEvolution(): void {
  console.log("\n=== Example 4: Quantum State Evolution ===");
  
  const machine = PvsNPMachineFactory.createSelfreferentialMachine();
  const tm = new QuantumTuringMachine(machine, "11", 30);
  
  const result = tm.run();
  
  console.log("Quantum state evolution:");
  for (let i = 0; i < Math.min(result.quantumStates.length, 8); i++) {
    const state = result.quantumStates[i];
    console.log(`  Step ${i}: entropy = ${toFixed(entropy(state), 4)}, coeffs = ${state.coeffs.size}`);
  }
  
  // Show quantum entanglement between states
  if (result.quantumStates.length >= 2) {
    const entanglement = tensor(result.quantumStates[0], result.quantumStates[result.quantumStates.length - 1]);
    console.log(`Initial-Final entanglement entropy: ${toFixed(entropy(entanglement), 4)}`);
  }
}

/**
 * Run all Turing machine examples
 */
export function runAllTuringMachineExamples(): void {
  console.log("🔧 Quantum-Enhanced Turing Machine Simulator");
  console.log("Demonstrating self-referential complexity in computation\n");
  
  demonstrateBasicTuringMachine();
  demonstrateBinarySearchMachine();
  demonstrateExponentialComplexity();
  demonstrateQuantumStateEvolution();
  
  console.log("\n✅ Turing machine simulator operational!");
  console.log("Phase 1 mathematical foundation layer complete!");
  console.log("Ready for Phase 2: SAT solver implementation.");
}