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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.

The Neighbour-sensing model refers to a conceptual framework or computational model utilized in various fields, including social sciences, biology, and computer science, to analyze interactions and relationships based on the presence and influence of neighboring entities. It can be applied in numerous contexts, but the specifics can vary depending on the discipline.

Nominal techniques, often referred to as Nominal Group Techniques (NGT), are structured methods used for group discussion and decision-making. They are designed to generate and prioritize ideas in a way that facilitates collaboration and ensures that all participants have an equal opportunity to contribute. NGT is typically used in settings such as meetings, workshops, or focus groups.

In computer science and economics, the term "nominal" typically refers to values that have not been adjusted for inflation or other factors. However, it's important to clarify the context, as "nominal terms" can have slightly different meanings in different areas. Here are two primary interpretations: 1. **Nominal vs.

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.

Probabilistic bisimulation is a concept used in the field of formal verification, particularly in the study of systems that exhibit probabilistic behavior, such as Markov processes, probabilistic transition systems, and other stochastic models. It extends the traditional notion of bisimulation, which is used in deterministic systems to compare the behavior of two state-transition systems. ### Key Concepts 1.

A "profinite word" generally refers to words that belong to the class of profinite objects in algebraic topology, specifically relating to certain types of algebraic structures that arise in the study of topological spaces. However, in a more common and broader context, "profinite word" might also refer to words that exhibit specific properties or patterns in a field of mathematics or theoretical computer science.

Promise theory is a conceptual framework used to understand the dynamics of cooperation and trust in relationships, organizations, and systems. Developed by Dr. Mark Burgess, it provides a way to model the interactions and agreements between different agents (which could be individuals, teams, organizations, or even software components) in terms of "promises." Key concepts of promise theory include: 1. **Promises**: These are commitments made by agents to other agents, signifying what they intend to deliver or do.

Pseudorandomness refers to the property of sequences of numbers that appear to be random but are generated by a deterministic process, typically using algorithms. These sequences are called pseudorandom sequences, and they are produced by mathematical algorithms known as pseudorandom number generators (PRNGs).

Quantum complexity theory is a branch of theoretical computer science that studies the complexity of problems within the framework of quantum computation. It explores how quantum algorithms can solve problems more efficiently than classical algorithms and seeks to classify problems based on their computational hardness in the quantum setting. Here are some key concepts and topics in quantum complexity theory: 1. **Quantum Computation Model**: Quantum complexity theory is grounded in the model of quantum computation, where computation is performed using quantum bits (qubits).

A Quantum Digital Signature (QDS) is a cryptographic technique that leverages the principles of quantum mechanics to provide secure digital signatures. It is designed to ensure the authenticity and integrity of digital messages in a way that is theoretically invulnerable to attacks from quantum computers, which can break many classical cryptographic protocols.

Quantum machine learning (QML) is an interdisciplinary field that combines concepts from quantum mechanics and machine learning. It explores how quantum computing can enhance machine learning algorithms and models, leveraging the unique properties of quantum systems to potentially solve problems that are infeasible for classical computers. Here are some key aspects of QML: 1. **Quantum Computers**: Unlike classical computers that use bits (0s and 1s), quantum computers use quantum bits or qubits.

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.

In the context of logic and formal systems, a **regular numerical predicate** typically refers to a type of predicate that deals with numerical properties or conditions. It can be used to describe a property or a condition that applies to numbers or the relationships between numerical values. However, the term “regular numerical predicate” could have various interpretations depending on the specific field or context in which it is used.

The Representer Theorem is a fundamental result in the field of machine learning and functional analysis, particularly in the context of regularized empirical risk minimization problems. It provides a bridge between high-dimensional data and solutions in a reproducing kernel Hilbert space (RKHS). ### Key Concepts: 1. **Empirical Risk Minimization:** This is the process of minimizing the empirical risk (or training error) over a dataset.

Rough set theory is a mathematical framework for dealing with uncertainty and vagueness in data analysis and knowledge representation. Introduced by Zdzisław Pawlak in the early 1980s, it provides a way to approximate sets when the information available is incomplete or imprecise. ### Key Concepts of Rough Set Theory: 1. **Indiscernibility Relation**: In rough set theory, objects are considered indiscernible if they cannot be distinguished based on the available attributes.

In the context of computer science, particularly in distributed systems, concurrency, and formal methods, **safety** and **liveness** are two fundamental properties used to describe the correctness and behavior of a system. They are often used in the analysis and design of protocols, algorithms, and systems. ### Safety Properties **Safety** properties assert that "something bad never happens." In other words, safety guarantees that certain undesirable states or conditions will not occur during the execution of a system.

The term "scientific community metaphor" typically refers to the way in which the scientific community is conceptualized and understood through various metaphors that capture its characteristics, dynamics, and functions. Metaphors allow us to simplify and communicate complex ideas about how scientists interact, share knowledge, and contribute to the advancement of science.