wiki_research

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

commit 7a171c6bf15dff68bbb0f585b1f648d4ccfe849a
parent 73e82cb51c41a0cdbe448840354ce7fc3be75e1a
Author: Antoine Amarilli <a3nm@a3nm.net>
Date:   Wed,  4 Mar 2026 09:32:07 +0100

commit with codex

Diffstat:
graph_h_minor_free | 2+-
nfa_unary_lengths | 2+-
regular_expression_repetition | 6++++++
regular_expression_repetition_intersection_nonemptiness | 5+++++
regular_expression_squaring | 6+++++-
regular_expression_squaring_universality | 10++++++++++
triangle_detection | 2++
triangle_detection_hfree_graphs | 7+++++++
universality_automata_nondeterministic | 4++--
9 files changed, 39 insertions(+), 5 deletions(-)

diff --git a/graph_h_minor_free b/graph_h_minor_free @@ -12,4 +12,4 @@ Up: [graph_free] See also: [graph_h_free] -Aliases: H minor free, minor free, H minor free graph, H minor free graphs, excluded minor, graph excluding minor, graphs excluding minor, graph excluding minors +Aliases: H minor free, minor free, H minor free graph, H minor free graphs, excluded minor, graph excluding minor, graphs excluding minor, graph excluding minors, H free graph, H free graphs diff --git a/nfa_unary_lengths b/nfa_unary_lengths @@ -11,4 +11,4 @@ An [NFA] which is [automata_unary], i.e., on a [unary_alphabet] Up: [automata_unary], [nfa_acceptance] -See also: [nfa_smallest_rejected] +See also: [nfa_smallest_rejected], [Universality_automata_nondeterministic] diff --git a/regular_expression_repetition b/regular_expression_repetition @@ -3,4 +3,10 @@ e^{p,q}: repeat e between p and q times - p and q written in binary (concise) +Special case: [regular_expression_squaring] + +Problems: +- [regular_expression_repetition_intersection_nonemptiness] +- for [language_universality], cf [regular_expression_squaring_universality] + Up: [regular_expression_extensions] diff --git a/regular_expression_repetition_intersection_nonemptiness b/regular_expression_repetition_intersection_nonemptiness @@ -0,0 +1,5 @@ +# Regular expression repetition intersection nonemptiness + +it is [PSPACE_complete], cf https://cstheory.stackexchange.com/a/57014 + +Up: [regular_expression_repetition], [Intersection_nonemptiness] diff --git a/regular_expression_squaring b/regular_expression_squaring @@ -2,6 +2,10 @@ [regular_expression] augmented with [squaring] operator -makes [language_inclusion] and [language_universality] [EXPSPACE_complete], cf https://cstheory.stackexchange.com/a/40250 +makes [language_inclusion] and [language_universality] [EXPSPACE_complete], cf [regular_expression_squaring_universality] + +but [intersection_nonemptiness] still in [PSPACE], like for [regular_expression_repetition], cf [regular_expression_repetition_intersection_nonemptiness] Up: [regular_expression], [squaring] + +See also: [regular_expression_repetition] diff --git a/regular_expression_squaring_universality b/regular_expression_squaring_universality @@ -0,0 +1,10 @@ +# Regular expression squaring universality + +It is [EXPSPACE_complete], cf https://cstheory.stackexchange.com/a/40250 +[meyer1972equivalence] + +Hence the same holds for [language_inclusion] and [language_equivalence] + +And the same holds for [regular_expression_repetition] + +Up: [language_universality], [regular_expression_squaring] diff --git a/triangle_detection b/triangle_detection @@ -13,6 +13,8 @@ https://en.wikipedia.org/wiki/Triangle-free_graph#Triangle_finding_problem - cf [williams2018subcubic] - cf https://people.csail.mit.edu/virgi/6.890/lecture2.pdf +- [triangle_detection_hfree_graphs] + Up: [computational_problem] on [graph], [conjunctive_query], [fine_grained_complexity_problems] See also: [all_edge_triangle], [boolean_matrix_multiplication], [sparse_triangle] diff --git a/triangle_detection_hfree_graphs b/triangle_detection_hfree_graphs @@ -0,0 +1,7 @@ +# Triangle detection in hfree graphs + +cf [abboud2026equivalent] + +Up: [triangle_detection], [H_free_graph] + +Aliases: Triangle detection in hfree graphs diff --git a/universality_automata_nondeterministic b/universality_automata_nondeterministic @@ -1,4 +1,4 @@ -# Universality automata nondeterministic +# Universality for nondeterministic automata [conp_complete] on [unary_alphabet] and [PSPACE_complete] otherwise: - https://cs.stackexchange.com/a/97751 @@ -8,4 +8,4 @@ Omega(n 2^n): cf [ellul2005regular], Theorem 32 Up: [universality_automata], [automata_nondeterministic] -Aliases: NFA universality +Aliases: NFA universality, Universality for nondeterministic automata