https://github.com/m4b/algos

Algebraic arithmetization of boolean algebra and its implementation.
https://github.com/m4b/algos

Last synced: 7 months ago
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Algebraic arithmetization of boolean algebra and its implementation.

• Host: GitHub
• URL: https://github.com/m4b/algos
• Owner: m4b
• License: gpl-3.0
• Created: 2013-08-14T01:21:46.000Z (almost 13 years ago)
• Default Branch: master
• Last Pushed: 2014-03-20T17:28:27.000Z (about 12 years ago)
• Last Synced: 2025-03-29T01:02:54.614Z (about 1 year ago)
• Language: OCaml
• Size: 449 KB
• Stars: 6
• Watchers: 4
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
algos

=====

 ἔνθ᾽ οἵ γ᾽ ἄλγε᾽ ἔχοντες ὑπὸ χθονὶ ναιετάοντες

 εἵατ᾽ ἐπ᾽ ἐσχατιῇ, μεγάλης ἐν πείρασι γαίης,

 δηθὰ μάλ᾽ ἀχνύμενοι, κραδίῃ μέγα πένθος ἔχοντες. 

 and he made them live beneath the wide-pathed earth,

 where they were afflicted, being set to dwell under the ground,

 at the end of the earth, at its great borders,

 in bitter anguish for a long time and with great grief at heart.

 Hesiod, Theogony, 620

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Algebraic arithmetization of boolean algebra and its OCaml implementation.

To compile:

ocamlbuild main.native

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A different kind of SAT solver, boolean formulas are represented as algebraic expressions.

For example:

a → b ≡ (1 + −a + (a × b))

The solver performs cancellation, idempotency reductions, x^2 = x holds in this algebra, and so on and so forth, until either a fully reduced algebraic expression in sum of product forms is found; or 0, or 1.  Reduction to 1 is a tautology, 0 a contradiction, and anything else a satisfiable expression.

The ``interpreter'' accepts unicode (∨, →, ¬, etc.), in addition to the usual ascii representations of the logical formulae (\/, ->, ~, etc.)