{"id":13992901,"url":"https://github.com/madvorak/vcsp","last_synced_at":"2025-10-24T06:06:48.096Z","repository":{"id":199217263,"uuid":"701420861","full_name":"madvorak/vcsp","owner":"madvorak","description":"General-Valued Constraint Satisfaction 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General-Valued Constraint Satisfaction Problems\n\nThis is a playground for experiments preceding our contribution to the [Lean 4](https://github.com/leanprover/lean4) version of [Mathlib](https://github.com/leanprover-community/mathlib4).\n\n[Permalink to the definition of VCSP in Mathlib](https://github.com/leanprover-community/mathlib4/blob/3e51ad145c59d7e879943907172a6c5a89d6420c/Mathlib/Combinatorics/Optimization/ValuedCSP.lean#L39)\n\nOur long-term goal is to formalize the dichotomy for fixed-template finite-valued constraint satisfaction problems [Thapper, Živný, Kolmogorov] while exploring potential generalizations (infinite domains, partially ordered codomains, and more).\n\n## Results (please see the definitions in [ValuedCSP.lean](https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Combinatorics/Optimization/ValuedCSP.lean) first)\n\n* [If a VCSP template over LinearOrderedCancelAddCommMonoid can express MaxCut, it cannot have any commutative fractional polymorphism.](https://github.com/madvorak/vcsp/blob/d9e00ac4cc6f790ec675b4c996cc56a4fd726a0d/VCSP/Hardness.lean#L70)\n* [Basic LP relaxation for VCSP over any OrderedRing of CharZero is valid.](https://github.com/madvorak/vcsp/blob/d9e00ac4cc6f790ec675b4c996cc56a4fd726a0d/VCSP/LinearRelaxation.lean#L261)\n* [If a VCSP template over ℚ has symmetric fractional polymorphisms of all arities, then Basic LP relaxation is tight.](https://github.com/madvorak/vcsp/blob/d9e00ac4cc6f790ec675b4c996cc56a4fd726a0d/VCSP/LinearRelaxationAndSFP.lean#L398)\n\n## Mathlib contributions that stem from this project\n\n### Pull requests (these PRs are compatible with each other)\n\n* https://github.com/leanprover-community/mathlib4/pull/7404\n* https://github.com/leanprover-community/mathlib4/pull/7893\n* https://github.com/leanprover-community/mathlib4/pull/7894\n* https://github.com/leanprover-community/mathlib4/pull/8707\n* https://github.com/leanprover-community/mathlib4/pull/9072\n* https://github.com/leanprover-community/mathlib4/pull/9307\n* https://github.com/leanprover-community/mathlib4/pull/9652\n* https://github.com/leanprover-community/mathlib4/pull/9838\n* https://github.com/leanprover-community/mathlib4/pull/10297\n* https://github.com/leanprover-community/mathlib4/pull/10379\n* https://github.com/leanprover-community/mathlib4/pull/11689\n* https://github.com/leanprover-community/mathlib4/pull/12806\n* https://github.com/leanprover-community/mathlib4/pull/12901\n* https://github.com/leanprover-community/mathlib4/pull/12903\n* https://github.com/leanprover-community/mathlib4/pull/12911\n* https://github.com/leanprover-community/mathlib4/pull/13167\n\n### Proposals for Linear Programming (these PRs are incompatible with each other)\n\n* https://github.com/leanprover-community/mathlib4/pull/7386\n* https://github.com/leanprover-community/mathlib4/pull/9693\n* https://github.com/leanprover-community/mathlib4/pull/10026\n* https://github.com/leanprover-community/mathlib4/pull/10159\n","funding_links":[],"categories":["Lean"],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmadvorak%2Fvcsp","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fmadvorak%2Fvcsp","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmadvorak%2Fvcsp/lists"}