Solvable Vs Unsolvable Problem Part-1

Duration: 10 min

This video lesson is available to enrolled students.

Return to /learn/MPPSC-ASSISTANT-PROFESSOR-COMPUTER-SCIENCE-PAPER-2/theory-of-computation/regular-language-properties/decidability-basics/asset-solvable-vs-unsolvable-problem-part-1 after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Paper 1 | General Studies: State Wise GK
  3. Paper 1 | Information and Communication Technology: Role of Internet and Web Services, Security in Mobile and Wireless Computing
  4. Paper 1 | Current Affairs: GK- Current Affairs
  5. Paper 2 | Discrete Mathematical Structure: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Probability
  6. Paper 2 | Digital Computer Organization And Architecture: Number System, Number Representation, Sequential Circuits, Combinational Circuit, Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer
  7. Paper 2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  8. Paper 2 | Programming Languages & Object-Oriented Programming Concepts: Java, OOPS with C++, Java Fundamentals, Array, String, IO & References
  9. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  10. Paper 2 | Data Structure And Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Advanced Algorithms
  11. Paper 2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS
  12. Paper 2 | Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
  13. Paper 2 | Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  14. Paper 2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization, Enhanced Data Models
  15. Paper 2 | Computer Network And Information Security: Introduction to CN, Data Communication, Application Layer, Hardware basics, Cyber Threats and Malware Attacks, Network Security, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP
  16. Paper 2 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  17. Paper 2 | Current Trends & Technologies: Emerging Tech Trends, Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Planning, Multi Agent Systems, Fuzzy Sets, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms, Artificial Intelligence, Data Warehousing & Mining, Electronic Data Interchange and E-Commerce, Terms & Abbreviations
  18. Paper 2 | Full Length Mock Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video lecture provides a foundational overview of computational problem classification and introduces the historical Konigsberg Bridge Problem. The instructor begins by presenting a hierarchical flowchart that categorizes all problems into Solvable and Unsolvable types. He further breaks down Solvable problems into Decidable and Undecidable categories, and finally into P Type and NP Type complexity classes. The lecture then transitions to graph theory, using the Konigsberg Bridge Problem as a case study. The instructor illustrates the physical layout of the city with its river and bridges, labeling landmasses A, B, C, and D. He demonstrates how to abstract this physical map into a mathematical graph, explaining the concept of traversing edges (bridges) exactly once. This segment highlights the origins of graph theory and the distinction between solvable and unsolvable problems in a practical context.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the broad classification of problems using a flowchart diagram. The top node is labeled 'PROBLEM', which branches into 'SOLVABLE' and 'UNSOLVABLE'. The instructor points to the 'PROBLEM' box and then the 'SOLVABLE' box, establishing the primary dichotomy. He explains that every problem in computer science falls into one of these two main categories. The visual aid clearly shows the hierarchy, setting the stage for a deeper dive into computability theory.

  2. 2:00 – 5:00 02:00-05:00

    The lecture delves deeper into the 'SOLVABLE' branch of the flowchart. The instructor draws red arrows connecting 'PROBLEM' to 'SOLVABLE' and 'UNSOLVABLE' to emphasize the relationship. He explains that 'SOLVABLE' problems are further divided into 'DECIDABLE' and 'UNDECIDABLE'. He notes that 'DECIDABLE' problems are those for which an algorithm exists that always halts with a correct yes or no answer. The flowchart also shows 'DECIDABLE' branching into 'P TYPE' and 'NP TYPE', indicating complexity classes. The instructor uses hand gestures to trace the path from the root problem down to these specific types.

  3. 5:00 – 10:00 05:00-10:00

    The topic shifts to the 'Konigsberg Bridge Problem'. The slide displays a diagram of the city with a river and seven bridges connecting four landmasses labeled A, B, C, and D. The instructor explains the challenge: to find a path that crosses every bridge exactly once. He then converts this physical map into a graph representation, drawing nodes for the landmasses and edges for the bridges. He draws the graph on the right side of the screen, showing nodes A, B, C, D connected by lines. He discusses how this problem was historically significant and led to the birth of graph theory, illustrating the concept of Eulerian paths and circuits.

  4. 10:00 – 10:02 10:00-10:02

    The video concludes with the graph of the Konigsberg Bridge Problem fully displayed on the screen. The instructor is likely summarizing the key takeaway that this problem, while seemingly simple, was unsolvable in its original form, reinforcing the earlier discussion on unsolvable problems. The visual focus remains on the graph with nodes A, B, C, D and the connecting edges, serving as a final visual anchor for the lesson on graph theory and problem solvability.

The lecture effectively connects abstract computational theory with concrete historical examples. It starts by defining the landscape of problems (Solvable vs. Unsolvable) and their sub-categories (Decidable, P, NP). It then grounds these concepts in the Konigsberg Bridge Problem, showing how a real-world scenario can be modeled as a graph. This progression helps students understand not just the definitions of solvability, but also the historical context and practical application of graph theory in determining whether a problem can be solved.

Loading lesson…