List of decidable languages. Decidable problems from language theory For simple machine models, such as finite automata or pushdown automata, many decision problems are solvable. Warm-Up: Some Decidable Languages Show that the following languages are decidable by describing (at a high level) an algorithm that decides them (see more in Sipser 4. Now suppose (for the purpose of a contradiction) that the set of undecidable lan- guages is also countable, i. This problem is related to the problem of recognizing and compiling programs in a programming language. What can we say about the halting set? We give algorithms for testing whether a finite automata accepts a string, whether the language of a finite automaton is empty, and whether two finite automata are equivalent. Recursive language In mathematics, logic and computer science, a recursive (or decidable) language is a recursive subset of the Kleene closure of an alphabet. Not all languages are decidable. (w ∈ L ↔ M accepts w) Mar 10, 2025 · The study of decidable languages is an important area of research in computer science and plays a critical role in developing algorithms and computational systems. We showed that there are only countably many such Turing Machines , so we may conclude that there are only countably many decidable languages . Recognizable vs. Equivalently, a formal language is recursive if there exists a Turing machine that decides the formal language. Decidable Languages Turing Machine M is called a recognizer for a language L over the alphabet Σ if the following statement is true: ∀w ∈ Σ∗. For this problem, we can easily find a solution by constructing an 1. By (c), the set of decidable languages is countable, so by Theorem 7 there is an enumeration of the decidable languages. In the case of deterministic finite automata, problems like equivalence can be solved even in polynomial time. There are two types of languages in the theory of computation (TOC), which are as follows − Decidable Undecidable A problem is called decidable, when there is a solution to that problem and also can construct algorithms corresponding to that. Feb 19, 2026 · Solution: By (d), there are uncountably many languages over a given alphabet Σ. e. Decidable Languages A Turing Machine M is called a recognizer for a language L over the alphabet Σ if the following statement is true: ∀w ∈ Σ∗. 2 & 5. We will denote this set by H and call it a halting set. a Turing Machine decider) to recognize it. A recursive language is a type of formal language that can be generated by the recursive grammar. If there is an algorithm that can decide membership in a language, that language is in R. Decidable Languages for decidability purposes, it is equivalent to present the Turing machine with a DFA, NFA, or a regular expression because the machines can convert from one form of encoding to another Decidable Languages In this section we give some examples of languages that are decidable by algorithms. Thursday, December 5/6, 2007 Reading: Sipser 4 and 5. Also there are efficient parsing algorithms for context-free grammars. By the Church-Turing thesis, any effective model of computation is equivalent in power to a Turing machine. We have shown that no algorithm is possible that, given a program p and data d, checks whether p halts on d. [1] Having said that I want to know the intuitive meaning of the decidable language. Delve into the principles of language decidability in automata theory, learn about decidable and undecidable languages, and their significance in computation. By definition, every language is either decidable or undecidable. 3 Revised Thursday, December 6 Solution : Since every decidable language requires a Turing Machine that decides it , decidable languages over a given alphabet Σ are in bijection with some subset of all Turing Machines over Σ . For example, we present an algorithm which tests whether a string is a member of a context-free language. Mar 8, 2011 · A language is “Turing-Decidable” iff there exists a Turing Machine such that when encountering a string in that language, the machine terminates and accepts that string; 1. Definition (Decidability) A language is decidable if there is an algorithm (i. , there is an Decidable and Undecidable Languages The Halting Problem and The Return of Diagonalization Wednesday. Jan 13, 2025 · Let’s examine the class of decidable languages in a bit more detail to see if we believe that it does correspond to the intuitive notion of computability that we want it to capture. With correct knowledge and ample experience, this question becomes very easy to solve. 1; Kozen 31; Stoughton 5. Example of Decidable Problem Find all the odd numbers in the range from 1 to 50. After reading various resources I could say that the DECIDABLE languages are: For all string s in the Languages L if there exists a Turing machine which HALTS either by ACCEPTING or REJECTING the string s. (w ∈ L ↔ M accepts w). 1) Jul 11, 2025 · Identifying languages (or problems*) as decidable, undecidable or partially decidable is a very common question in GATE. In language terms, this means that the set of all pairs (p; d) for which p halts on d is not decidable. bjn ehk csv kzo gtf svd fqu icl dik ema rmh eal pwn szr kwa