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A '''Decider''' (or a '''Filter''') is a program which attempts to decide whether or not a given [[Turing machine]] (TM) will halt. Since the Halting Problem is uncomputable, no decider can decide all TMs, instead deciders categorize each TM into one of three categories: Halting, Proven Infinite, or [[Holdout]]. | A '''Decider''' (or a '''Filter''') is a program which attempts to decide whether or not a given [[Turing machine]] (TM) will halt. Since the Halting Problem is uncomputable, no decider can decide all TMs, instead deciders categorize each TM into one of three categories: Halting, Proven Infinite, or [[Holdout]]. | ||
There are a wide variety of methods used to construct deciders. Some broad categories are: [[Accelerated Simulator]]s, [[ | There are a wide variety of methods used to construct deciders. Some broad categories are: [[Accelerated Simulator]]s, [[Backward Reasoning]] and [[Closed Set]] methods. | ||
== List of Deciders == | == List of Deciders == | ||
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* [[Translated Cycler]] | * [[Translated Cycler]] | ||
* [[Backward Reasoning]] | * [[Backward Reasoning]] | ||
* [[Closed Position Set (CPS) | * [[Closed Position Set]] (CPS) | ||
* [[Closed Tape Language]] (CTL) | * [[Closed Tape Language]] (CTL) | ||
* [[Finite Automata Reduction (FAR) | * [[Finite Automata Reduction]] (FAR) | ||
* [[Inductive Proof System]] | * [[Inductive Proof System]] | ||
* [[Bouncer]] | * [[Bouncer]] | ||
* [[Halting Segment]] | * [[Halting Segment]] | ||
* [[Cycler]] | |||
== See also == | == See also == | ||
https://bbchallenge.org/method#deciders | https://bbchallenge.org/method#deciders | ||
Latest revision as of 15:48, 8 October 2025
A Decider (or a Filter) is a program which attempts to decide whether or not a given Turing machine (TM) will halt. Since the Halting Problem is uncomputable, no decider can decide all TMs, instead deciders categorize each TM into one of three categories: Halting, Proven Infinite, or Holdout.
There are a wide variety of methods used to construct deciders. Some broad categories are: Accelerated Simulators, Backward Reasoning and Closed Set methods.
List of Deciders
- Translated Cycler
- Backward Reasoning
- Closed Position Set (CPS)
- Closed Tape Language (CTL)
- Finite Automata Reduction (FAR)
- Inductive Proof System
- Bouncer
- Halting Segment
- Cycler