A formal language is a set of strings composed of symbols from a defined alphabet that follows specific syntactical rules or grammar. Unlike natural languages, which are used for everyday communication and can be ambiguous and variable, formal languages are precise and unambiguous. They are often used in mathematical logic, computer science, linguistics, and theoretical computer science. Key characteristics of formal languages include: 1. **Alphabet**: The basic set of symbols from which strings are formed.

Occam learning, often associated with the principle of Occam's Razor, refers to a concept in machine learning and statistical modeling that suggests choosing the simplest model among competing hypotheses that adequately explains the data. The idea is based on the philosophical principle attributed to William of Ockham, which states that one should not multiply entities beyond necessity; in a scientific context, it implies that the simplest explanation is often the best.

In the context of formal languages, a "pattern language" is a concept that can refer to a way of describing syntactical structures or rules that are used in the formation of strings within a formal language. While the term does not refer to a standardized concept in formal language theory per se, it is often associated with the following ideas: 1. **Regular Expressions**: Patterns are commonly used with regular expressions, which are sequences of characters that define a search pattern.

In group theory, which is a branch of abstract algebra, a **coset** is a concept used to describe a way of partitioning a group into smaller, equally structured subsets. Cosets arise when considering a subgroup within a larger group.

The ACM Doctoral Dissertation Award is a prestigious recognition given by the Association for Computing Machinery (ACM) to honor outstanding doctoral dissertations in the field of computer science and information technology. This award aims to highlight the significance and impact of research conducted by doctoral candidates, as well as to promote high-quality work in the computing community.

The British Colloquium for Theoretical Computer Science (BCTCS) is an annual conference that focuses on theoretical aspects of computer science. It serves as a forum for researchers, academics, and students to present and discuss their latest findings and developments in this field. The topics covered at BCTCS typically include areas such as algorithms, computational complexity, formal languages, automata theory, and other foundational topics in computer science.

A **Bigraph** is a mathematical structure used primarily in the field of graph theory and computer science, particularly in the context of modeling systems and their interactions. The term "bigraph" typically refers to a bipartite graph that consists of two types of vertices, which can represent different entities or components of a system, and edges that represent relationships or interactions between these entities.

Bio-inspired computing refers to a subset of computational methods and algorithms that are inspired by biological processes and systems. This approach draws on principles observed in nature, including the behaviors and functionalities of living organisms, to solve complex problems in computer science and engineering. Key aspects of bio-inspired computing include: 1. **Genetic Algorithms**: These algorithms mimic the process of natural selection and evolution. They use mechanisms such as mutation, crossover, and selection to optimize solutions to problems.

Motion planning is a field in robotics and computer science that involves determining a sequence of valid configurations or movements that an object, typically a robot or autonomous agent, must follow in order to move from a starting position to a desired goal position while avoiding obstacles and adhering to certain constraints. The process can involve complex calculations to ensure that the path taken is feasible given the limitations of the robot, such as its kinematics, dynamics, and environmental factors.

Natural computing is an interdisciplinary field that draws from various areas of science and computer science to develop computational models and algorithms inspired by nature. This field seeks to utilize natural processes, concepts, and structures to solve complex computational problems. The core idea is to mimic or draw inspiration from biological, physical, and chemical systems to create new computational techniques.

Bisimulation is a concept in the field of concurrency theory and formal methods, particularly in the study of transition systems and processes. It is a relationship between state-transition systems that allows us to determine if two systems behave similarly in a formal sense. The idea is to compare two systems based on their ability to mimic each other's behavior, particularly in terms of their possible state transitions.

The Flajolet Prize is an award given in recognition of outstanding contributions to the field of algorithmic research, specifically in the area of combinatorial algorithms and analysis of algorithms. It is named after Philippe Flajolet, a prominent researcher known for his work in combinatorics and algorithms. The prize is typically awarded at the International Conference on Analysis of Algorithms (ALA), where leading researchers in the field gather to present their work.

Granular computing is a computational paradigm that focuses on processing, representing, and analyzing information at varying levels of granularity. This concept is based on the idea that data can be divided into smaller, meaningful units (or "granules") where each granule can represent specific types of knowledge or decision-making processes. The main goal is to manage complexity by allowing computations and problem-solving approaches to be performed at different levels of detail or abstraction.

Quasi-empiricism in mathematics refers to an approach that emphasizes empirical data and experiences in the development of mathematical theories and concepts, although it does not adhere strictly to the empirical methods seen in the natural sciences. This perspective recognizes the role of intuition, observation, and practical examples in the formulation and understanding of mathematical ideas, while still maintaining a certain level of abstraction and rigor typically associated with formal mathematics.

Categorical logic is a branch of logic that deals with categorical propositions, which are statements that relate to the relationships between classes or categories of objects. In categorical logic, we analyze how different groups (or categories) can be included in or excluded from one another based on the propositions we make. The core elements of categorical logic include: 1. **Categorical Propositions**: These are statements that affirm or deny a relationship between two categories or classes.

The Circuit Value Problem (CVP) is a decision problem in computer science, particularly in the fields of complexity theory and cryptography. In general terms, the problem can be described as follows: Given a Boolean circuit (a network of logical gates) and a specific input assignment, the goal is to determine the output of the circuit for that input.

Coinduction is a mathematical and theoretical concept primarily used in computer science, particularly in the areas of programming languages, type theory, and formal verification. It provides a framework for defining and reasoning about potentially infinite structures, such as streams or infinite data types. In more formal terms, coinduction can be seen as a dual to induction.

The term "complexity function" can refer to several concepts depending on the context in which it is used. Here are some interpretations across different fields: 1. **Computer Science (Complexity Theory)**: In computational complexity theory, a complexity function often refers to a function that describes the resource usage (time, space, etc.) of an algorithm as a function of the size of its input.

Computation refers to the process of performing mathematical operations or processing information according to a defined set of rules or algorithms. It encompasses a wide variety of activities, from simple arithmetic calculations to complex problem-solving tasks performed by computers. Key aspects of computation include: 1. **Algorithms**: These are step-by-step procedures or formulas for solving problems. Algorithms form the basis of computation, guiding how inputs are transformed into outputs.

In the context of quantum computing, "concurrence" is a measure of quantum entanglement, particularly applicable to mixed states of two qubits. Concurrence quantifies how much two qubits are entangled, which is a crucial concept in understanding the capabilities and behaviors of quantum systems.