In logic, finite model theory, and computability theory, Trakhtenbrot's theorem (due to Boris Trakhtenbrot) states that the problem of validity in first-order logic on the class of all finite models is undecidable.
People also ask
What is the Büchi Elgot Trakhtenbrot theorem?
In formal language theory, the Büchi–Elgot–Trakhtenbrot theorem states that a language is regular if and only if it can be defined in monadic second-order logic (MSO): for every MSO formula, we can find a finite-state automaton defining the same language, and for every finite-state automaton, we can find an MSO formula ...
What is the Borodin's gap theorem?
In computational complexity theory, the Gap Theorem, also known as the Borodin–Trakhtenbrot Gap Theorem, is a major theorem about the complexity of computable functions. It essentially states that there are arbitrarily large computable gaps in the hierarchy of complexity classes.
In formal language theory, the Büchi–Elgot–Trakhtenbrot theorem states that a language is regular if and only if it can be defined in monadic second-order ...
Apr 15, 2020 · We study finite first-order satisfiability (FSAT) in the constructive setting of dependent type theory.
One of the first results, sometimes regarded as the birth of finite model theory, is Trakhtenbrot's result from 1950 stating that validity over finite models is ...
Jun 24, 2020 · Item (1) implies that we can justify the undecidability of a target problem by reduction from a seed problem known to be undecidable, such as ...
Apr 15, 2013 · But the theorem holds for any relational vocabulary with at least one binary relation symbol and also it should not depend on the machine M.
Jun 6, 2020 · Item (1) implies that we can justify the undecidability of a target problem by reduction from a seed problem known to be undecidable, such as ...
Apr 29, 2021 · Abstract:We study finite first-order satisfiability (FSAT) in the constructive setting of dependent type theory.
It is undecidable if an arbi- trary sentence of first-order logic has a finite model (i.e., is finitely satisfiable). Proof. Suppose there were a Turing machine ...
Jun 17, 2022 · we present a streamlined proof strategy for Trakhtenbrot's theorem well-suited for mecha- nisation and simple to explain informally, basing on ...