wiki_research

personal research wiki
git clone https://a3nm.net/git/wiki_research/
Log | Files | Refs

commit 00c1b56dccfd065ebf6f92e8d28f8c72eb5f3a50
parent 19e1dc5c3e83c41fb9c31da689d8e768a5e6dd05
Author: Antoine Amarilli <a3nm@a3nm.net>
Date:   Fri,  9 Oct 2026 00:19:19 +0200

commit with codex

Diffstat:
automaton_intersection | 2+-
chase_termination | 2+-
chromatic_number | 7+++++++
chromatic_number_computation | 5+++++
circuit_parameter | 2++
complexity_class | 1+
graph_coloring | 7+------
grid_minor | 2+-
hypertree_width_computation | 9+++++++++
hypertree_width_variants | 2+-
linear_extension | 2++
linear_extension_counting | 2++
property_testing_formal_language | 1+
pspace_complete | 3+++
qbf_sat | 7+++++++
treelike_data | 2+-
16 files changed, 45 insertions(+), 11 deletions(-)

diff --git a/automaton_intersection b/automaton_intersection @@ -7,4 +7,4 @@ can be done with [product_construction] Up: [automaton_constructions], [language_intersection] -See also: [regular_expression_conjunction], [CFG_intersection] +See also: [regular_expression_conjunction], [CFG_intersection], [intersection_nonemptiness] diff --git a/chase_termination b/chase_termination @@ -4,7 +4,7 @@ depends on the kind of [chase]: - [chase_oblivious]: [oblivious_chase_termination] - [chase_restricted]: [restricted_chase_termination] -depends on whether you want all instances or an input instance +depends on whether you want [all_instance_termination] or [data_dependent_chase_termination] [academic_papers]: - [gogacz2014all] diff --git a/chromatic_number b/chromatic_number @@ -0,0 +1,7 @@ +# Chromatic number + +The least number of colors for [graph_coloring] of a graph + +[chromatic_number_computation] + +Up: [graph_coloring], [graph_parameter] diff --git a/chromatic_number_computation b/chromatic_number_computation @@ -0,0 +1,5 @@ +# Chromatic number computation + +The [computation_problem], given an [undirected_graph], of computing its [chromatic_number] + +Up: [computation_problem], [chromatic_number] diff --git a/circuit_parameter b/circuit_parameter @@ -6,3 +6,5 @@ - [circuit_size] Up: [parameter] of [circuit] + +See also: [graph_parameter] diff --git a/complexity_class b/complexity_class @@ -25,6 +25,7 @@ - [l_poly] L/poly - [optimization_problem] - [NPO] +- [incremental_complexity] ## Results diff --git a/graph_coloring b/graph_coloring @@ -26,12 +26,7 @@ ## Complexity -- [np_complete], already for [graph_planar] and [4_regular] graphs - - [np_complete] to find if it is 3 or 4 - - 4 colors on [planar_graph] is always feasible by the [four_color_theorem] -- [3_coloring] is in [linear_time] by [Brook's_theorem] on [graphs] of maximal [degree] 3 - - see https://cstheory.stackexchange.com/questions/51368/which-hypergraphs-can-be-simplified-by-alternatively-removing-a-hyperedge-and-an -- [bipartiteness_testing] (k=2) +[graph_coloring_computation] ## Constructions diff --git a/grid_minor b/grid_minor @@ -12,6 +12,6 @@ used for [hardness] results, e.g., [grohe2007complexity] Up: [theorem] about [grid_graph] -See also: [grid_minor_directed], [treewidth] +See also: [grid_minor_directed], [treewidth], [polynomial_grid_minor_theorem] Aliases: grid minor extraction, grid extraction diff --git a/hypertree_width_computation b/hypertree_width_computation @@ -0,0 +1,9 @@ +# Hypertree width computation + +for any k, we can determine in [PTIME] whether an input [hypergraph] has [hypertreewidth] <= k, and if so compute a [hypertree_decomposition]: [gottlob2002hypertree] + +[parameterized_complexity]: [gottlob2005hypertree] + +Up: [hypertree_width], [computation_problem] + +See also: [treewidth_computation] diff --git a/hypertree_width_variants b/hypertree_width_variants @@ -2,7 +2,7 @@ - [generalized_hypertree_width], with [edge_cover] - [hypertree_width] (and [hypertree_decomposition]) with [special_condition] on the projected variables - - makes [tree_decomposition_computation] easier + - makes [hypertree_width_computation] and [tree_decomposition_computation] easier - [query_decomposition] all are within a factor 3 of each other, cf [adler2007hypertree] and [gottlob2007generalized] diff --git a/linear_extension b/linear_extension @@ -7,3 +7,5 @@ Asymptotics of the number of elements required to achieve a specific number of l Up: [partial_order] Aliases: linear extensions + +See also: [order_polynomial] diff --git a/linear_extension_counting b/linear_extension_counting @@ -3,4 +3,6 @@ [brightwell1991counting]: it's [SharpP_complete] - also for [height_2_posets], cf [dittmer2018counting] +It is [W1_hard] when parameterized by the [treewidth] of the [cover_graph], cf [eiben2019counting] + Up: [counting_problem], [linear_extension] diff --git a/property_testing_formal_language b/property_testing_formal_language @@ -15,6 +15,7 @@ - [francois2015streaming] on [visibly_pushdown_languages] - [fischer2010approximate] for [edit_distance_with_moves] - called "approximate satisfiability" +- [jackman2026query] for [dyck_languages] and generalizations Up: [property_testing], [formal_language] diff --git a/pspace_complete b/pspace_complete @@ -2,4 +2,7 @@ The class of [computational_problems] that are in [PSPACE] and [PSPACE_hard] +- [QBF_SAT] +- [NFA_universality] + Up: [pspace] diff --git a/qbf_sat b/qbf_sat @@ -0,0 +1,7 @@ +# QBF SAT + +[SAT] on [QBF] + +It is [PSPACE_complete] + +Up: [QBF], [SAT] diff --git a/treelike_data b/treelike_data @@ -6,4 +6,4 @@ On such data we can do [pqe_mso] Up: [data] of bounded [treewidth], [types_of_data] -See also: [bounded_treewidth_graph], [pathlike_data] +See also: [bounded_treewidth_graph], [pathlike_data], [bounded_treewidth_sets]