Theoretical Aspects of Computer Science Advanced Lectures 1st Edition by Gholamreza B Khosrovshahi, Ali Shokoufandeh ISBN 9783540433286 by Charles J. Colbourn (auth.), Gholamreza B. Khosrovshahi, Ali Shokoufandeh, Amin Shokrollahi (eds.) 3540433287 instant download after payment.
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ISBN 13: 9783540433286
Author: Gholamreza B Khosrovshahi, Ali Shokoufandeh
TheFirstSummerSchoolonTheoreticalAspectsonComputerSciencewasheld attheInstituteforStudiesinTheoreticalPhysicsandMathematics(IPM)from July3-10,2000. Theideaoforganizingasummerschoolwasoriginatedduringaconversation betweenthe?rstandthesecondeditorofthisvolumeinthewinterof2000at IPMinTehran. ThedecisionwasformalizedwhenthethirdeditorvisitedIPM laterinthewinter. ThemainideabehindtheSummerSchoolwastointroducetothestudents in Iran some of the highly innovative and promising research in Theoretical ComputerScience, and, atthesametime, tostarta?owofideasbetweentop researchersinthe?eldandtheIranianscientists. Forthisreason, thetalkswere designedtobeofatutorialstyle. Theorganizersdecidedtoconcentrateonafewimportantareasofresearch in modern Theoretical Computer Science. To attract students to this imp- tant area, they also decided to include talks on applications of methods from TheoreticalComputerSciencetootherareas. ThisvolumecontainsthewrittencontributionstotheprogramofthisS- mer School. It is intended for students and researchers who want to gain - quaintancewithcertaintopicsinTheoreticalComputerScience. Thepaperson quantumcomputation, approximationalgorithms, self-testing/correcting, al- braic modeling of data, and the Regularity Lemma correspond to the former category, whileconnectionsbetweenmultipleaccesscommunicationandcom- natorialdesigns, graph-theoreticalmethodsincomputervision, andlow-density parity-checkcodesbelongtothelattercategory. Eachcontributiontothisvolumewaspresentedinatwohoursession, l- vingampletimeforquestionsanddiscussions. Thetutorialswerefollowedbya numberofspecializedtalkstouchingoncurrentresearchproblemsinthearea. Partsofthetalkshavebeenincorporatedintothematerialofthecontributions. January2002 G. B. Khosrovshahi A. Shokoufandeh A. Shokrollahi Organization The ?rst International Summer School on Theoretical Aspects of Computer Science was organized by the Institute for Studies in Theoretical Physics and Mathematics(IPM)inTehran, Iran. ProgramCommittee ConferenceChair: G. B. Khosrovshahi, IPMandtheUniversity ofTehran, Iran A. Shokoufandeh, DrexelUniversity, USA A. Shokrollahi, DigitalFountain, USA Local Arrangements: M. Zamani SponsoringInstitutions SchoolofMathematics, Institutefor Studies in Theoretical Physics and Mathematics(IPM), Tehran, Iran World Mathematical Year (WMY) 2000 National Commission Service de Coop´ eration et d' Action Culturelle, AmbassadedeFranceen Iran Neda Rayaneh Institute (NRI) http: //www. neda. net. ir VIII Acknowledgements WearegratefultoProfessorM. J. Larijani, thedirectorofIPM, whohasbeen a great advocate for the expansion of Theoretical Computer Science at the - stitute, andhelpedussecuremajorfundingfromIPM. Wewouldalsoliketo expressourthankstoProfessorS. Shahshahani, theDeputyDirectorofIPM, who was most helpful in soliciting ?nancial support from the World Mathe- tical Year 2000 National Commission. The Service de Coop´ eration et d' Action Culturelle of the French embassy in Iran kindly provided travel funds for our invited speakers from France. We thank the Service Culturelle for their generous support. Finally, wewouldliketoexpressourgratitudetoM.
Theoretical Aspects of Computer Science Advanced Lectures 1st Table of contents:
Part I: Foundations of Computation and Complexity
Chapter 1: Advanced Automata Theory and Formal Languages
- Review of Finite Automata and Regular Languages (brief)
- Pushdown Automata and Context-Free Languages: Advanced Topics
- Pumping Lemma for CFLs
- Chomsky Normal Form and Greibach Normal Form
- Deterministic vs. Non-Deterministic PDA
- Turing Machines: Variants and Equivalences
- Multi-Tape, Multi-Head, Non-Deterministic TMs
- Universal Turing Machines
- Linear Bounded Automata and Context-Sensitive Languages
- Chomsky Hierarchy: Deeper Insights and Closure Properties
Chapter 2: Computability Theory: Limits of Algorithms
- Undecidability:
- The Halting Problem and its Proofs
- Rice's Theorem
- Post Correspondence Problem
- Reductions: Many-One and Turing Reducibility
- Recursion Theory:
- Primitive Recursive Functions, General Recursive Functions
- Church-Turing Thesis Revisited
- Arithmetical Hierarchy and Degree Theory (Turing Degrees)
- The Busy Beaver Problem and Incomputability
Chapter 3: Computational Complexity Theory: What is Feasible?
- Complexity Classes: P, NP, PSPACE, EXPTIME, L, NL, NC, AC
- NP-Completeness and NP-Hardness:
- Cook-Levin Theorem
- Reductions and Proving NP-Completeness
- Famous NP-Complete Problems (SAT, TSP, Knapsack, etc.)
- Space Complexity:
- Savitch's Theorem
- Log-Space Reductions
- Hierarchy Theorems (Time and Space)
- Probabilistic Complexity Classes: RP, Co-RP, BPP, PP
- Interactive Proof Systems: IP=PSPACE
- Cryptographic Implications of Complexity Theory
Part II: Advanced Algorithms and Data Structures
Chapter 4: Algorithmic Paradigms and Advanced Design Techniques
- Amortized Analysis
- Randomized Algorithms:
- Las Vegas vs. Monte Carlo Algorithms
- Hashing, Quicksort, Min-Cut
- Approximation Algorithms:
- PTAS, FPTAS, APX
- Vertex Cover, Set Cover, TSP Approximations
- Online Algorithms and Competitive Analysis
- Dynamic Programming: Beyond Basic Applications (e.g., Matrix Chain Multiplication, Optimal BST)
Chapter 5: Graph Algorithms: Structure and Flow
- Network Flow: Max-Flow Min-Cut Theorem and Algorithms (Ford-Fulkerson, Edmonds-Karp, Dinic)
- Bipartite Matching and its Relation to Flow
- Min-Cost Max-Flow
- Graph Separators and Treewidth
- Advanced Shortest Path Algorithms: All-Pairs Shortest Path (Floyd-Warshall, Johnson's Algorithm)
- Planar Graphs and Embeddings
Chapter 6: Data Structures for Efficiency and Specialization
- Advanced Tree Structures: Red-Black Trees, AVL Trees, B-Trees, Splay Trees
- Heaps: Fibonacci Heaps, Pairing Heaps
- Disjoint Set Data Structures (Union-Find)
- Skip Lists
- String Data Structures: Suffix Trees, Suffix Arrays
- Geometric Data Structures: K-D Trees, Quadtrees
Part III: Specialized Theoretical Domains
Chapter 7: Quantum Computing and Information Theory
- Quantum Bits (Qubits) and Quantum Gates
- Superposition and Entanglement
- Quantum Algorithms:
- Deutsch-Jozsa Algorithm
- Grover's Algorithm (Search)
- Shor's Algorithm (Factoring)
- Quantum Complexity Classes (BQP)
- Introduction to Quantum Error Correction
Chapter 8: Cryptography and Security Foundations
- Public-Key Cryptography: RSA, ElGamal, Elliptic Curve Cryptography
- Digital Signatures and Authentication
- Hash Functions and Message Authentication Codes (MACs)
- Zero-Knowledge Proofs
- Secure Multi-Party Computation
- Post-Quantum Cryptography Challenges
Chapter 9: Distributed Algorithms and Concurrency
- Models of Distributed Computing (Synchronous, Asynchronous)
- Consensus Algorithms: Paxos, Raft
- Leader Election
- Distributed Mutual Exclusion
- Consistency Models (Sequential, Causal, Eventual)
- Fault Tolerance: Byzantine Fault Tolerance
Chapter 10: Logic in Computer Science
- Propositional and First-Order Logic (Review and Advanced Proof Systems)
- Modal Logic and Temporal Logics (LTL, CTL) for System Verification
- Automata on Infinite Words (Büchi Automata)
- Model Checking (symbolic model checking, bounded model checking)
- Satisfiability Modulo Theories (SMT) Solvers
Chapter 11: Algorithmic Game Theory and Mechanism Design
- Game Theory Fundamentals: Nash Equilibrium, Dominant Strategies
- Price of Anarchy and Price of Stability
- Algorithmic Mechanism Design:
- Online Learning in Games
- Social Choice Theory and Arrow's Impossibility Theorem
Conclusion: The Evolving Landscape of Theoretical Computer Science
- Major Open Problems in TCS (P vs. NP, Unique Games Conjecture, etc.)
- Interdisciplinary Connections and Future Directions
- The Role of Theory in Advancing Practical Computing
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