Undecidable problem

About: Undecidable problem is a research topic. Over the lifetime, 3135 publications have been published within this topic receiving 71238 citations.

The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions

Abstract: Many cyberinformaticians would agree that, had it not been for amphibious epistemologies, the refinement of randomized algorithms might never have occurred [114, 114, 188, 62, 114, 62, 70, 179, 68, 95, 54, 188, 152, 95, 191, 59, 168, 148, 99, 152]. In this work, we disprove the deployment of cache coherence [58, 129, 128, 106, 154, 51, 176, 164, 76, 59, 134, 203, 193, 116, 65, 24, 123, 109, 48, 177]. Leat, our new system for reliable models, is the solution to all of these issues.

Some Algorithmic Problems for ε-algebras

Abstract: The word problem1, stated relative to one or another algebraic system, has attracted the attention of many mathematicians. In the works of A.A. Markov [1] and E. Post [3] it was proved for the first time that there exist algebraic systems (semigroups) with undecidable word problem. The most significant achievement in this direction is the result of P.S. Novikov [2] that establishes undecidability of the word problem for groups. In 1950, A.I. Zhukov [5], while studying free nonassociative algebras, established that in the case in which one does not assume that the algebra satisfies any identical relation (for instance, associativity) the word problem (as well as some other algorithmic problems) is decidable. From the results obtained for semigroups, it easily follows that the word problem is undecidable for associative algebras.

Bounded Quantification Is Undecidable

Abstract: F? is a typed ?-calculus with subtyping and bounded second-order polymorphism. First introduced by Cardelli and Wegner, it has been widely studied as a core calculus for type systems with subtyping. We use a reduction from the halting problem for two-counter Turing machines to show that the subtyping and typing relations of F? are undecidable.

Bounded quantification is undecidable

Abstract: F≤ is a typed l-calculus with subtyping and bounded second-order polymorphism. First proposed by Cardelli and Wegner, it has been widely studied as a core calculus for type systems with subtyping.Curien and Ghelli proved the partial correctness of a recursive procedure for computing minimal types of F≤ terms and showed that the termination of this procedure is equivalent to the termination of this procedure is equivalent to the termination of its major component, a procedure for checking the subtype relation between F≤ types. This procedure was thought to terminate on all inputs, but the discovery of a subtle bug in a purported proof of this claim recently reopened the question of the decidability of subtyping, and hence of typechecking.This question is settled here in the negative, using a reduction from the halting problem for two-counter Turing machines to show that the subtype relation of F≤ is undecidable.

Handbook of computability theory

Abstract: Part 1: Fundamentals of Computability Theory. Part 2: Reducibilities and Degrees. Part 3: Generalized Computability Theory. Part 4: Mathematics and Computability Theory. Part 5: Logic and Computability Theory. Part 6: Computer Science and Computability Theory.