## Logic and abstract automata

Automata Theory is an exciting, theoretical branch of computer science. It established its roots during the 20th Century, as mathematicians began developing - both theoretically and literally - machines which imitated certain features of man, completing calculations more quickly and reliably. The word automaton itself, closely related to the word "automation", denotes automatic processes carrying out the production of specific processes.

Simply stated, automata theory deals with the logic of computation with respect to simple machines, referred to as automata.

Through automata, computer scientists are able to understand how machines compute functions and solve problems and more importantly, what it means for a function to be defined as computable or for a question to be described as decidable.

Automatons are abstract models of machines that perform computations on an input by moving through a series of states or configurations.

At each state of the computation, a transition function determines the next configuration on the basis of a finite portion of the present configuration. As a result, once the computation reaches an accepting configuration, it accepts that input.

The most general and powerful automata is the Turing machine. The major objective of automata theory is to develop methods by which computer scientists can describe and analyze the dynamic behavior of discrete systems, in which signals are sampled periodically.

The behavior of these discrete systems is determined by the way that the system is constructed from storage and combinational elements. Characteristics of such machines include:. The families of automata above can be interpreted in a hierarchal form, where the finite-state machine is the simplest automata and the Turing machine is the most complex.

The focus of this project is on the finite-state machine and the Turing machine. A Turing machine is a finite-state machine yet the inverse is not true. The exciting history of how finite automata became a branch of computer science illustrates its wide range of applications.

The first people to consider the concept of a finite-state machine included a team of biologists, psychologists, mathematicians, engineers and some of the first computer scientists.

Garmin sdkThey all shared a common interest: to model the human thought process, whether in the brain or in a computer. Warren McCulloch and Walter Pitts, two neurophysiologists, were the first to present a description of finite automata in Their paper, entitled, "A Logical Calculus Immanent in Nervous Activity", made significant contributions to the study of neural network theory, theory of automata, the theory of computation and cybernetics.

Later, two computer scientists, G.Program analysis based on set constraints has many potential applications, including compiler optimisations, type-checking, debugging, verification and planning.

The usual approach to set constraint analysis is to solve a set of constraints derived directly from the program text. However, it was pointed out by Cousot and Cousot that set constraint analysis of a particular program P could be understood as an abstract interpretation over a finite domain of nondeterministic tree automata, constructed from P.

One advantage of doing this is that set constraint analysis can be combined with other domains, using standard frameworks for abstract interpretation.

In this paper we define such an abstract interpretation for logic programs, and describe its implementation. Both goal-dependent and goal-independent analysis are considered. Variations on the abstract domains operations are introduced, and we discuss the associated tradeoffs of precision and complexity.

The experimental results presented indicate that the proposed approach is of practical interest. Documents: Advanced Search Include Citations. GallagherGerman Puebla.

How to move xref in autocadAbstract Program analysis based on set constraints has many potential applications, including compiler optimisations, type-checking, debugging, verification and planning.

Powered by:.In theoretical computer science and mathematicsthe theory of computation is the branch that deals with how efficiently problems can be solved on a model of computationusing an algorithm.

The field is divided into three major branches: automata theory and languages, computability theoryand computational complexity theorywhich are linked by the question: "What are the fundamental capabilities and limitations of computers? In order to perform a rigorous study of computation, computer scientists work with a mathematical abstraction of computers called a model of computation.

There are several models in use, but the most commonly examined is the Turing machine. So in principle, any problem that can be solved decided by a Turing machine can be solved by a computer that has a finite amount of memory. The theory of computation can be considered the creation of models of all kinds in the field of computer science.

Therefore, mathematics and logic are used. In the last century it became an independent academic discipline and was separated from mathematics. Automata theory is the study of abstract machines or more appropriately, abstract 'mathematical' machines or systems and the computational problems that can be solved using these machines. These abstract machines are called automata.

Automata theory is also closely related to formal language theory, [5] as the automata are often classified by the class of formal languages they are able to recognize. An automaton can be a finite representation of a formal language that may be an infinite set. Automata are used as theoretical models for computing machines, and are used for proofs about computability. Language theory is a branch of mathematics concerned with describing languages as a set of operations over an alphabet.

It is closely linked with automata theory, as automata are used to generate and recognize formal languages. There are several classes of formal languages, each allowing more complex language specification than the one before it, i. Chomsky hierarchy[6] and each corresponding to a class of automata which recognizes it. Because automata are used as models for computation, formal languages are the preferred mode of specification for any problem that must be computed.

Computability theory deals primarily with the question of the extent to which a problem is solvable on a computer. The statement that the halting problem cannot be solved by a Turing machine [7] is one of the most important results in computability theory, as it is an example of a concrete problem that is both easy to formulate and impossible to solve using a Turing machine. Much of computability theory builds on the halting problem result. Another important step in computability theory was Rice's theoremwhich states that for all non-trivial properties of partial functions, it is undecidable whether a Turing machine computes a partial function with that property.

Computability theory is closely related to the branch of mathematical logic called recursion theorywhich removes the restriction of studying only models of computation which are reducible to the Turing model. Complexity theory considers not only whether a problem can be solved at all on a computer, but also how efficiently the problem can be solved. Two major aspects are considered: time complexity and space complexity, which are respectively how many steps does it take to perform a computation, and how much memory is required to perform that computation.

In order to analyze how much time and space a given algorithm requires, computer scientists express the time or space required to solve the problem as a function of the size of the input problem. For example, finding a particular number in a long list of numbers becomes harder as the list of numbers grows larger.

If we say there are n numbers in the list, then if the list is not sorted or indexed in any way we may have to look at every number in order to find the number we're seeking.

### Logic, semigroups and automata on words

We thus say that in order to solve this problem, the computer needs to perform a number of steps that grows linearly in the size of the problem. To simplify this problem, computer scientists have adopted Big O notationwhich allows functions to be compared in a way that ensures that particular aspects of a machine's construction do not need to be considered, but rather only the asymptotic behavior as problems become large.

Perhaps the most important open problem in all of computer science is the question of whether a certain broad class of problems denoted NP can be solved efficiently.

Aside from a Turing machineother equivalent See: Churchâ€”Turing thesis models of computation are in use. In addition to the general computational models, some simpler computational models are useful for special, restricted applications. Regular expressionsfor example, specify string patterns in many contexts, from office productivity software to programming languages.

Another formalism mathematically equivalent to regular expressions, Finite automata are used in circuit design and in some kinds of problem-solving. Context-free grammars specify programming language syntax. Non-deterministic pushdown automata are another formalism equivalent to context-free grammars. Primitive recursive functions are a defined subclass of the recursive functions.

Different models of computation have the ability to do different tasks. One way to measure the power of a computational model is to study the class of formal languages that the model can generate; in such a way to the Chomsky hierarchy of languages is obtained.Several famous classes have been classified within this logic.

We briefly review the main results concerning second order, which covers classes like PH, NP, P, etc.

**Abstract Reasoning-Logic Reasoning- CSE-NAPOLCOM REVIEW**

In particular, we survey the results and fascinating open problems dealing with the first-order quantifier hierarchy. We also discuss the first-order logic of one successor and the linear temporal logic.

## Automata, Logic and Games: Theory and Application

There are in fact three levels of results, since these logics can be interpreted on finite words, infinite words or bi-infinite words. The paper is self-contained. In particular, the necessary background on automata and finite semigroups is presented in a long introductory section, which includes some very recent results on the algebraic theory of infinite words.

This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Almeida, Implicit operations on finite J -trivial semigroups and a conjecture of I.

Simon, J. Pure Appl. Algebra 69 â€” Beauquier, Bi-limites de langages reconnaissables, Theor. Beauquier, Ensembles reconnaissables de mots bi-infinis, in: Automata on Infinite Wordsed. Beauquier and M.

How to install onesync fivemNivat, About rational sets of factors of a bi-infinite word, in: Automata, Languages and Programminged. Beauquier and J. Pin, Factors of words, in: Automata, Languages and Programmingeds. Ausiello, M. Dezani-Ciancaglini and S.Handbook of Formal Languages pp Cite as. The subject of this chapter is the study of formal languages mostly languages recognizable by finite automata in the framework of mathematical logic.

Unable to display preview. Download preview PDF. Skip to main content. Advertisement Hide. Languages, Automata, and Logic. This process is experimental and the keywords may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access.

Alur, D. A theory of timed automata, Theor. Aho, J. Hoperoft, J.

Arnold, D. Nivat, A. Podelski, Eds. Google Scholar. Barrington, K. Compton, H. Straubing, D. System Sci. Hansel, C. Michaux, R.Sign in Create an account. Syntax Advanced Search. About us. Editorial team. Michael A. Journal of Symbolic Logic 37 2 Logic and Philosophy of Logic. Edit this record. Mark as duplicate. Find it on Scholar. Request removal from index. Revision history.

Asus fx505gtFrom the Publisher via CrossRef no proxy Setup an account with your affiliations in order to access resources via your University's proxy server Configure custom proxy use this if your affiliation does not provide a proxy. Configure custom resolver. Ronald Endicott - - Philosophical Studies 1 Genaro J. Dynamic Dependency Grammar. David Milward - - Linguistics and Philosophy 17 6 - Non-Wellfounded Set Theory.

Lawrence S. Moss - - Stanford Encyclopedia of Philosophy. Book Reviews. Bar-HillelRobert L. Brody - - Philosophia 4 1 Review: Michael A. Arbib, Theories of Abstract Automata. Review: M.

Schutzenberger, Finite Counting Automata; M. Schutzenberger, Certain Elementary Families of Automata. Rabin - - Journal of Symbolic Logic 34 2 Review: V.Mathematical logic and automata theory are two scientific disciplines with a fundamentally close relationship.

The authors of Logic and Automata take the occasion of the sixtieth birthday of Wolfgang Thomas to present a tour d'horizon of automata theory and logic. The twenty papers in this volume cover many different facets of logic and automata theory, emphasizing the connections to other disciplines such as games, algorithms, and semigroup theory, as well as discussing current challenges in the field.

Wiskundige logica en automata theorie zijn twee wetenschappelijke disciplines die nauw met elkaar verbonden zijn.

Faaaloalo faasamoaDeze relatie is niet alleen fundamenteel voor velen theoretische resultaten, maar vormt ook de basis voor een coherente methodologie voor de controle en synthese van gegevensverwerkingssystemen. De auteurs van Logic en Automata grijpen de gelegenheid van de zestigste verjaardag van Wolfgang Thomas aan om een 'tour d'horizon' op het gebied van automata theory en logica te geven.

### Languages, Automata, and Logic

De twintig hiervoor verzamelde essays beslaan verschillende facetten van de logica en automata theorie, ze benadrukken de verbanden met andere disciplines als complexiteitstheorie, games, algorithms en semi-groep theorie en bespreken eigentijdse uitdagingen op dit gebied.

Location of Repository. Logic and Automata : History and Perspectives By. Topics: wetenschap algemeen, popular science, PD. OAI identifier: oai:oapen Suggested articles.

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