Lecture

Theory of Computability: Solvability and Complexity

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Description

This lecture introduces the theory of computability, focusing on the solvability of problems by algorithms. Starting with defining what constitutes a 'problem', the instructor discusses examples and the distinction between problems solvable in finite time and those that are not. The lecture delves into decision problems and the famous Halting Problem, demonstrating its undecidability through a proof by contradiction. It then explores complexity classes, particularly P and NP, highlighting the difference between problems solvable in polynomial time and those verifiable in polynomial time. Examples of problems belonging to each class are provided, emphasizing the challenges posed by NP-complete problems. The lecture concludes with a discussion on the 'P vs. NP' problem, a million-dollar question in computer science.

Official source

Ontological neighbourhood

Theoretical computer science

Theory of computation: Computational complexity theory

Related concepts (32)

NP (complexity)

In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems. NP is the set of decision problems for which the problem instances, where the answer is "yes", have proofs verifiable in polynomial time by a deterministic Turing machine, or alternatively the set of problems that can be solved in polynomial time by a nondeterministic Turing machine. NP is the set of decision problems solvable in polynomial time by a nondeterministic Turing machine.

Communication

Communication is usually defined as the transmission of information. The term can also refer to the message itself, or the field of inquiry studying these transmissions, also known as communication studies. The precise definition of communication is disputed. Controversial issues are whether unintentional or failed transmissions are included and whether communication does not just transmit meaning but also create it. Models of communication aim to provide a simplified overview of its main components and their interaction.

Mass communication

Mass communication is the process of imparting and exchanging information through mass media to large population segments. It utilizes various forms of media as technology has made the dissemination of information more efficient. Primary examples of platforms utilized and examined include journalism and advertising. Mass communication, unlike interpersonal communication and organizational communication, focuses on particular resources transmitting information to numerous receivers.

Nonverbal communication

Nonverbal communication (NVC) is the transmission of messages or signals through a nonverbal platform such as eye contact, facial expressions, gestures, posture, use of objects and body language. It includes the use of social cues, kinesics, distance (proxemics) and physical environments/appearance, of voice (paralanguage) and of touch (haptics). A signal has three different parts to it, including the basic signal, what the signal is trying to convey, and how it is interpreted.

Media (communication)

In mass communication, media are the communication outlets or tools used to store and deliver information or data. The term refers to components of the mass media communications industry, such as print media, publishing, the news media, photography, cinema, broadcasting (radio and television), digital media, and advertising. The development of early writing and paper enabling longer-distance communication systems such as mail, including in the Persian Empire (Chapar Khaneh and Angarium) and Roman Empire, can be interpreted as early forms of media.

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