Chapter
The Satisfiability Problem and Complexity Theory
47:34 - 1:02:10 (14:36)
In this episode, the host explains how the satisfiability problem of propositional logic is a universal combinatorial problem and describes Stephen Cook's contribution to complexity theory. The episode also discusses the difficulty of finding cliques.
Clips
Verifying a clique to see if it reaches a target number of vertices is an easy problem, while finding the clique itself is a hard problem.
47:34 - 50:17 (02:43)
Summary
Verifying a clique to see if it reaches a target number of vertices is an easy problem, while finding the clique itself is a hard problem. The difficulty in finding the clique makes it challenging to determine if a clique of a specific size exists in a given graph.
ChapterThe Satisfiability Problem and Complexity Theory
Episode#111 – Richard Karp: Algorithms and Computational Complexity
PodcastLex Fridman Podcast
The P vs. NP problem is considered the most central problem in theoretical computer science, combinatorial algorithm theory, and computational complexity theory.
50:17 - 57:11 (06:53)
Summary
The P vs. NP problem is considered the most central problem in theoretical computer science, combinatorial algorithm theory, and computational complexity theory. The problem asks if P is equal to NP and it is still unsolved.
ChapterThe Satisfiability Problem and Complexity Theory
Episode#111 – Richard Karp: Algorithms and Computational Complexity
PodcastLex Fridman Podcast
The satisfiability problem of propositional logic is a universal combinatorial problem, where any algorithm can be expressed as a sequence of moves of the Turing machine.
57:11 - 1:02:10 (04:59)
Summary
The satisfiability problem of propositional logic is a universal combinatorial problem, where any algorithm can be expressed as a sequence of moves of the Turing machine. This means that any non-deterministic polynomial time algorithm can be translated into the language of the satisfiability problem.