Artificial Intelligence
“Master state space search, A* heuristic proofs, CSPs, Minimax alpha-beta pruning, first-order logic resolution, and Bayesian network d-separation for GATE DA.”
A comprehensive, mathematically rigorous study notebook covering classical artificial intelligence. Spans uninformed and informed search, A* admissibility and consistency proofs, local optimization, constraint satisfaction (AC-3), adversarial game theory (Minimax, Alpha-Beta), formal logic theorem proving (CNF, Skolemization, MGU Unification, Resolution Refutation), and probabilistic graphical models (Bayesian Networks, d-separation, Markov blankets, variable elimination). Engineered from first principles specifically for high-percentile GATE Data Science & AI (DA) preparation.
Structured Notes & Exam Lens
A · B.Tech Structured Study Sequence
5 Sections · Full CurriculumUninformed & Informed State Space Search
State space search formulation, uninformed graph traversals (BFS, DFS, UCS, IDS), heuristic design, A* admissibility and consistency proofs, and heuristic dominance.
Problem formulation, BFS, DFS, Uniform Cost Search (Dijkstra), and Iterative Deepening (IDS) performance bounds.
f(n) = g(n) + h(n), proving A* optimality on trees vs graphs, and dominance of heuristics.
Local Search & Constraint Satisfaction Problems (CSP)
Local search landscapes, Hill Climbing, Simulated Annealing temperature schedules, Genetic Algorithms, CSP formulation, Arc Consistency (AC-3), and Backtracking heuristics.
State space landscapes, plateaus, ridges, Simulated Annealing Metropolis acceptance probability, and Genetic Algorithms.
CSP formalization, Arc Consistency (AC-3), MRV, Degree heuristic, and Least Constraining Value.
Adversarial Search & Game Theory
Two-player zero-sum perfect information games, Minimax decision trees, Alpha-Beta pruning cutoffs, evaluation functions, and games with chance (Expectiminimax).
Alpha (MAX lower bound) >= Beta (MIN upper bound) triggers immediate subtree cutoff.
Chance nodes, expected value propagation, and evaluation function linearity constraints.
Propositional & First-Order Logic Reasoning
Propositional logic, truth tables, satisfiability (SAT), Horn clauses, Forward/Backward Chaining, First-Order Logic, Skolemization, Most General Unifier (MGU), and Resolution Refutation.
Logical entailment KB |= alpha, CNF conversion, Horn clauses, and linear-time chaining algorithms.
Converting to clausal form, Most General Unifier (MGU), and proving theorems via contradiction.
Probabilistic Reasoning & Bayesian Networks
Bayesian belief networks, conditional independence, d-separation rules (chains, forks, colliders), Markov blankets, and exact probabilistic inference via Variable Elimination.
DAG factorization, d-separation over chains/forks/colliders, and Markov blanket boundaries.
Inference by enumeration, Variable Elimination factor algebra, and Likelihood Weighting sampling.
B · GATE 2027 Syllabus Scope
Official syllabus scope and related lesson coverage; topics outside the syllabus are marked as enrichment.
- •Uninformed search strategies: Breadth-first search, depth-first search, uniform cost search, depth-limited search, iterative deepening search
- •Informed search algorithms: Greedy best-first search, A* search, heuristic evaluation functions, admissibility, consistency, heuristic dominance
- •Local search and optimization: Hill climbing variations, simulated annealing, genetic algorithms
- •Constraint satisfaction problems (CSP): Node consistency, arc consistency (AC-3 algorithm), backtracking with MRV, degree, and LCV heuristics
- •Adversarial search: Two-player zero-sum games, minimax algorithm, alpha-beta pruning, evaluation functions, games with chance (expectiminimax)
- •Propositional logic: Syntax, semantics, truth tables, validity, satisfiability, logical entailment, CNF conversion, Horn clauses, forward and backward chaining
- •First-order logic: Quantifiers, models, interpretations, clausal form conversion, Skolemization, Most General Unifier (MGU), resolution refutation
- •Reasoning under uncertainty: Conditional probability, Bayes' rule, Bayesian belief networks, conditional independence, d-separation, Markov blanket, variable elimination
Interactive Labs & Verified PYQs
Revision & Rapid Review Sheets
Authoritative Textbooks & Video Lectures
All notes in this notebook cross-reference standard academic literature. We do not pretend student notes substitute for classical texts — they guide you through them.
Curated lectures from verified educators (Gate Smashers, Neso Academy, Knowledge Gate, and MIT OCW) selected specifically for difficult concept visualizations.
These notes are open and maintained together.
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