Computational Theory Study Cards

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Computational Theory

A branch of computer science that deals with the study of algorithms, automata, and complexity theory.

Algorithms

Step-by-step procedures or instructions for solving a problem or performing a task.

Automata Theory

The study of abstract machines and computational models, including finite automata, pushdown automata, and Turing machines.

Turing Machines

A theoretical computing device that can simulate any algorithm and is used to understand the limits of computation.

Computability

The study of what can and cannot be computed, and the limits of computation.

Complexity Theory

The study of the inherent complexity of computational problems and the resources required to solve them.

P vs NP Problem

One of the most famous open problems in computer science, asking whether every problem whose solution can be verified quickly can also be solved quickly.

Formal Languages

Languages with precise rules and structures, often used to describe programming languages and communication protocols.

Regular Expressions

A sequence of characters that defines a search pattern, used for pattern matching in strings.

Context-Free Grammars

A formal grammar in which every production rule is of the form A -> α, where A is a nonterminal symbol and α is a string of terminals and nonterminals.

Pushdown Automata

A type of automaton that can use a stack to store information and is more powerful than finite automata.

Turing Machine Variants

Different variations of Turing machines that have additional capabilities or restrictions.

Decidability

The property of a problem being solvable by an algorithm, either by producing the correct answer or indicating that no solution exists.

Undecidability

The property of a problem being unsolvable by an algorithm, meaning that there is no algorithm that can always produce the correct answer.

Reductions

Techniques used to show that one problem can be transformed into another problem, often used to prove the hardness of problems.

Time Complexity

The amount of time required by an algorithm to run as a function of the input size.

Space Complexity

The amount of memory required by an algorithm to run as a function of the input size.

NP-Completeness

A property of computational problems that are at least as hard as the hardest problems in the class NP.

Approximation Algorithms

Algorithms that find solutions that are close to the optimal solution for optimization problems.

Randomized Algorithms

Algorithms that use randomization to improve efficiency or simplify the design.

Cryptography

The practice of secure communication in the presence of adversaries, often involving encryption and decryption.

Quantum Computing

A field of computing that uses quantum mechanics to perform certain computations more efficiently than classical computers.

Computational Learning Theory

The study of how machines can learn from data and improve their performance on specific tasks.

Parallel Computing

The use of multiple processors or computers to solve a computational problem more quickly.

Distributed Computing

The use of multiple computers or nodes to solve a computational problem by dividing the work among them.

Computational Geometry

The study of algorithms and data structures for geometric problems, such as finding the intersection of two lines.

Graph Algorithms

Algorithms that operate on graphs, such as finding the shortest path or detecting cycles.

Network Flows

Algorithms that model the flow of resources through a network, such as finding the maximum flow or minimum cut.

Linear Programming

A mathematical optimization technique for finding the best outcome in a linear mathematical model, subject to constraints.

Integer Programming

A mathematical optimization technique for finding the best outcome in a linear mathematical model with integer variables, subject to constraints.

Combinatorial Optimization

The study of optimization problems over discrete structures, such as finding the best arrangement of objects or the shortest path in a graph.

Game Theory

The study of mathematical models of strategic interaction between rational decision-makers.

Data Structures

Organized and structured formats for storing and manipulating data efficiently, such as arrays, linked lists, and trees.

Sorting Algorithms

Algorithms that arrange a list of elements in a particular order, such as ascending or descending.

Searching Algorithms

Algorithms that find the position of a target value within a list or data structure.

Dynamic Programming

A method for solving complex problems by breaking them down into simpler overlapping subproblems.

Greedy Algorithms

Algorithms that make locally optimal choices at each step with the hope of finding a global optimum.

Divide and Conquer

A problem-solving technique that involves breaking a problem into smaller subproblems, solving them independently, and combining the solutions.

Graph Theory

The study of mathematical structures used to model pairwise relations between objects, such as nodes and edges.

Tree Algorithms

Algorithms that operate on tree structures, such as finding the lowest common ancestor or performing tree traversals.

String Algorithms

Algorithms that operate on strings, such as pattern matching or string manipulation.

Numerical Algorithms

Algorithms that solve numerical problems, such as finding roots of equations or solving systems of linear equations.

Matrix Algorithms

Algorithms that operate on matrices, such as matrix multiplication or finding eigenvalues and eigenvectors.

Geometric Algorithms

Algorithms that solve geometric problems, such as computing convex hulls or finding the closest pair of points.

Network Algorithms

Algorithms that operate on network structures, such as finding the shortest path or detecting cycles in a network.

Parallel Algorithms

Algorithms that can be executed simultaneously on multiple processors or computers to solve a computational problem more quickly.

Distributed Algorithms

Algorithms that can be executed on multiple computers or nodes to solve a computational problem by dividing the work among them.