automata theory
Automata theory is a branch of the theory of computation and one of the most important theories in computer science. By studying abstract computer models such as finite state machines (FSMs), pushdown automata, and Turing machines, automata theory is applied to solve problems in formal languages, formal grammars, computability, computability, and natural language processing.
The central concepts of automata theory are automata and state transitions, where automata are abstract models of computers that receive inputs, change states, and produce outputs.
In automata theory, different types of automata have different computational and representational capabilities. A finite state automaton (FSM) has a finite number of states and can be a computational machine that changes its state and produces an output when it receives an input.
Automata theory is closely related to formal language theory, which can determine the classes of languages that a particular automaton can accept and the existence and construction of automata that produce a given formal language. It is also important in the fields of computational theory and algorithms, where it is applied to the design of algorithms using automata and the verification of programs. Furthermore, it is widely used in fields such as natural language processing and cognitive science. Automata theory includes important concepts such as methods of theoretical analysis of automata and language hierarchies that can determine the classes of languages that a particular automaton can accept.
automaton
In computer science, an automaton is an abstract form of a computer model that takes an input and modifies its internal state to produce an output. There are different types of automata, including finite state automata (FSM), pushdown automata, and Turing machines.
A finite state automaton (FSM) is one of the most basic types of automaton, having a finite number of states and receiving inputs to change states and produce outputs An FSM consists of the following three elements.
- Input alphabet: the set of inputs that the automaton accepts.
- State set: the set of states an automaton can take.
- Transition function: a function that allows an automaton to take the current state and input and transition to the next state.
FSMs are used in a variety of applications. Examples include communication protocols, hardware circuit design, text processing, natural language processing, and speech recognition.
Pushdown automata (PDAs) are stacks (LIFO data structures) added to FSMs,
The Turing machine will be a computer model based on infinitely long tapes and state transitions in the FSM.
These automata are more expressive than FSMs and can solve more complex problems.
automaton (quantum mechanics)
A finite automaton (FA) is a computational model that takes an input string and processes it according to certain rules. A finite automaton is represented using a finite state diagram (FSD), which takes an input string and transitions from one state to another.
Finite automata are mainly classified into the following two types.
- Deterministic Finite Automaton (DFA)
- Non-deterministic Finite Automaton (NFA)
DFA becomes a finite automaton whose next state is critically determined by the current state and the input character. In other words, whether the input string is recognized or not is always determined by the same state transition diagram. On the other hand, NFA can transition to multiple states depending on the current state and the input character, and there are multiple possibilities as to whether it will be recognized or not.
Finite automata are used in natural language processing, compilers, and databases, for example, for searching strings using regular expressions and parsing programming languages. They may also be used in engineering applications such as semiconductor design automation, communication protocol design, and syntactic analysis, as well as in biology and artificial intelligence research, where state machines (groups) are used to model neural systems, and in linguistics, where they model the grammar of natural languages.
FSM
A finite state machine (FSM) is a type of computer that transitions states with respect to an input sequence. diagram to change the current state upon receiving an input and generate the appropriate output.
FSMs are classified into three main types
- FSM without memory (Moore type): returns only the current state as output
- FSM with memory (Mealy type): generates output based on current state and input
- Deterministic FSM (DFA): uniquely transitions to the next state based on the current state and input.
The FSM is designed by creating a state transition diagram. This state transition diagram is a graph that represents the relationship between states and transitions, and the rules for state transitions in response to inputs.
FSMs are widely used in the design of digital circuits, programming languages, and communication protocols. It is used, for example, in file system control, electronics control, language processing, and data compression. The FSM is also a fundamental tool in automata theory and computation theory, and will be used in fields such as machine learning and artificial intelligence.
Petri-net
Petri nets are a type of automata theory and can be one of the graphical modeling languages used for modeling concurrent systems. Petri nets were invented by Carl Adam Petri in 1962 and are widely used in fields such as industrial control and software engineering.
Petri nets consist of two types of elements: one is a place and the other is a transition.
Places represent states with a number of tokens, called markings. Tokens can represent, for example, products, parts, data, etc. A transition represents a change of state in which a token can be taken from a place and placed in another place. Transitions can have both inputs and outputs.
Petri nets have the following properties.
- Orthogonality: There are no constraints between transitions, so multiple transitions can fire simultaneously.
- Reversibility: Marking can return to a previous state.
- Configurability: Complex systems with multiple subsystems can be modeled.
Petri nets are used in many areas, including modeling concurrent systems, distributed systems, communication protocols, and database transactions. They are also used as workflow models and business process models, and may be used to improve the efficiency of business processes.
automatic sequencing
Automated Planning is a technology that automatically generates a sequence of actions to reach a certain goal state. Automated planning has been studied in the fields of computer science, artificial intelligence, and robotics.
Automated planning generally consists of the following three elements
- State: Represents the current state of the problem. A state consists of attributes such as objects, resources, and their states.
- Action: represents an action taken to solve a problem. Actions have preconditions and effects. Preconditions are necessary conditions for executing an action, and effects are states that are changed by the action.
- Goal : represents the final state required to solve the problem.
The automatic plan will generate a sequence of actions to reach the target state from the current state based on the above elements. Specifically, the automatic plan will calculate the sequence of actions required to get from the current state to the target state.
Automatic planning is used in a wide range of fields, including scheduling, control, problem solving, robot motion planning, business process automation, and medical diagnosis. It is also one of the most fundamental problems in the field of artificial intelligence and is sometimes applied in combination with machine learning and optimization.
In this blog, we provide information on automata, state transitions, Petri nets, and automatic programming, including theory, concrete examples of use, and implementation.
Counting Problem and Combinatorial Optimization
Counting problems (counting problems) are one of the problems frequently tackled in mathematics, such as combinatorics and probability theory, which are tasks often associated with finding the number of combinations or permutations as a problem of counting the total number of objects satisfying certain conditions.
These problems are solved using mathematical principles and formulas, and concepts such as permutations, combinations, and binomial coefficients are often used, and depending on the problem, the respective formula must be chosen according to the nature of the problem.
Automata
Automata theory is a branch of the theory of computation and one of the most important theories in computer science. By studying abstract computer models such as finite state machines (FSMs), pushdown automata, and Turing machines, automata theory is applied to solve problems in formal languages, formal grammars, computability, computability, and natural language processing. This section provides an overview of this automata theory, its algorithms and various applications and implementations.
- Overview of the Aho-Hopcroft-Ullman Algorithm and Related Algorithms and Examples of Implementations
The Aho-Hopcroft-Ullman Algorithm (Aho-Hopcroft-Ullman Algorithm) is known as an efficient algorithm for string processing problems such as string search and pattern matching. This algorithm combines the basic data structures in string processing, Trie and Finite Automaton, to efficiently search for patterns in strings, and is mainly used for string matching, but also has applications in compilers, text search engines, and other It is mainly used for string matching, but has applications in a wide range of fields, including compilers and text search engines.
Finite State Machine (FSM) Technology
A Finite State Machine (FSM) is a type of computer that transitions states with respect to an input sequence. diagram to change the current state upon receiving an input and generate the appropriate output.
Behavior Tree is a framework for building complex AI behaviors that also appear in game AI. Originally developed for robotics, it is now used as an improved hierarchical state machine for designing AI for non-player characters (NPCs) in games such as FPS. The advantage is that it is easy to design and implement, reusable and portable, and can accommodate large and complex logics.
Petri-net technology
Petri nets are a descriptive model of discrete event systems proposed by Petri in 1962, which will represent the relationship between asynchronous and parallel events and the states that guide them in event-driven systems. Petri Net is a graphical model of states and transitions, and is a very flexible and general modeling language consisting of four structural elements: place P, transition T, input relation I, output relation O (PTIO) and marking M. In this article, we will give an overview of Petri Net, its applications, concrete implementations, and reference books.
AutoPlanning Technology
An AutoPlanning problem is a problem of planning a series of actions necessary to achieve a certain goal. Specifically, it is an algorithm that determines the sequence of actions to start from a certain state and reach a target state.
Dynamic Programming is a mathematical method for solving optimization problems, especially those with overlapping subproblems. Dynamic programming provides an efficient solution method because it dramatically reduces the amount of exponential computation by saving and reusing the results once computed. This section describes various algorithms and specific implementations in python for this dynamic programming.
Mixed integer optimization is a type of mathematical optimization and refers to problems that simultaneously deal with continuous and integer variables. The goal of mixed integer optimization is to find optimal values of variables under constraints when maximizing or minimizing an objective function. This section describes various algorithms and implementations for this mixed integer optimization.
This paper presents a simple, sound, complete, and systematic algorithm for domain-independent STRIPS planning. Simplicity is achieved by starting with a basic procedure and applying a general, independently verifiable lifting transformation. Previous planners have been designed directly as lifted procedures. Our ground procedure is the ground version of Tate’s NONLIN procedure: in Tate’s procedure, it is not necessary to determine whether the preconditions of the steps in the unfinished plan are guaranteed to hold for all linearizations. This allows the Tate procedure to avoid the use of Chapman’s modal truth criterion. Systematics is the property that the same plan or subplan is never considered more than once.
Counting Problems and Combinatorial Optimization
- Counting Problem Overview, Algorithm and Implementation Examples
Counting problems (counting problems) are one of the most frequently tackled problems in mathematics, such as combinatorics and probability theory, which are tasks often associated with finding the number of combinations or permutations as a problem of counting the total number of objects satisfying certain conditions. These problems are solved using mathematical principles and formulas, and concepts such as permutations, combinations, and binomial coefficients are often used, and depending on the problem, the respective formula must be chosen according to the nature of the problem.
Combinatorial optimization theory has been applied to many real-world problems such as transportation planning, scheduling, placement, combinatorial problems, and optimization problems. The problem is to find a subset of a set consisting of a certain number of elements that satisfies a set of constraints and to find the best solution among them. It is one of the mathematical methods to deal with discrete optimization problems to find the optimal solution under certain constraints.
- Overview of Optimization by Integer Linear Programming (ILP) and Examples of Algorithms and Implementations
Integer Linear Programming (ILP) is a method for solving mathematical optimization problems, especially for finding integer solutions under constraints. ILP is a type of Linear Programming (LP) with the additional conditions that the objective function and constraints are linear and the variables take integer values.
Digital Game AI Technology
Intelligent human-machine interaction has long been practiced in the world of games. In this article, we first summarize its history as a base for thinking about it, picking up information from “Digital Game Textbook: The Latest Trends in the Game Industry You Should Know”.
In this article, I would like to discuss the autonomous agents that emerged in the last generation (after FY00).
The quality of a digital game character AI is determined by “how much control over time and space the AI can exercise. This also means how much it can recognize its surroundings and how much it can construct its actions within a certain time range and time scale. For each of these, we will discuss the corresponding technology.
The next important perception, time, is very important to view AI from the perspective of time in digital games. To give AI the perception of time axis, it is first necessary to provide it with the past (memory), which requires securing a storage space (memory) and determining its memory format, which determines its intellectual foundation.
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