commit 688e14adc4587b0685aa765969021b141a027a0e
parent bb747ae4a92411679392c8372d21dd3e3e8089ce
Author: Antoine Amarilli <a3nm@a3nm.net>
Date: Fri, 26 Sep 2025 09:39:29 +0200
commit with codex
Diffstat:
8 files changed, 29 insertions(+), 1 deletion(-)
diff --git a/context_free_grammar_linear b/context_free_grammar_linear
@@ -7,6 +7,8 @@ https://en.wikipedia.org/wiki/Linear_grammar
- [linear_CFG_equivalence]
- Testing [language_emptiness] of [intersection] is already [undecidable] by reduction from [post_correspondence_problem]
+By [Greibach's_theorem], it is undecidable whether an input [CFG] recognizes a [linear_CFL]
+
Up: [context_free_grammar]
Aliases: linear grammar, linear grammars, linear context-free grammar, linear context-free grammars, linear CFG, linear CFGs
diff --git a/context_free_language_linear b/context_free_language_linear
@@ -6,6 +6,8 @@ Special cases:
- [unambiguous_linear_CFL]
- [deterministic_linear_CFL]
+By [Greibach's_theorem], it is undecidable whether an input [CFG] recognizes a [linear_CFL]
+
Up: [context_free_language]
Aliases: linear context-free language, linear context-free languages, linear CFL, linear CFLs
diff --git a/crpq b/crpq
@@ -4,6 +4,7 @@
- [RPQ]
- [CQ]
- [Boolean_CRPQ]
+- [CRPQ_acyclic]
[Generalizations]:
- [C2RPQ]
diff --git a/fagin1983degrees b/fagin1983degrees
@@ -4,7 +4,6 @@
- [beta_acyclic]
- [lanzinger2021tractability]
- [gamma_acyclic]
- - cf [delpia2018multilinear]
- [berge_acyclic]
Up: [academic_paper] about [hypergraph_acyclicity]
diff --git a/gamma_acyclic b/gamma_acyclic
@@ -0,0 +1,6 @@
+# Gamma acyclic
+
+- cf [delpia2018multilinear]
+- cf [atserias2025gamma]
+
+Up: [fagin1983degrees]
diff --git a/k_ambiguous_cfg b/k_ambiguous_cfg
@@ -5,9 +5,16 @@ A *k-ambiguous CFG* is a [CFG] where every [word] has at most k [parse_trees]
Special cases:
- k=1: [uCFGs]
- k=2: [2_ambiguous_CFGs]
+- they exist for each value of k, cf [naji1998grad] p9
It is an [open_problem] whether every k-ambiguous CFG can be written as a [language_union] of k [uCFGs], but within [bounded_CFGs] this is known to be true, cf [wich2005ambiguity] p181 point (iv).
+[Computational_problems]:
+- [CFG_inclusion]: [undecidable], in fact already [undecidable] for [linear_uCFGs]
+- [CFG_equivalence]: [open_problem] whether it is [decidable], in fact already open for [UCFGs]
+- [CFG_universality]: [undecidable], because testing if there is a word in the [intersection] of two [linear_UCFGs] is [undecidable] (by coding [Turing_machines] using [baker1974reversal])
+- counting the number of words in the [k_slice]: this is [sharpP1_hard] by [bertoni1991complexity]
+
Up: [k_ambiguous], [CFG]
See also: [infinitely_ambiguous_CFG], [Degree_of_ambiguity_cfg]
diff --git a/rpq_output_sensitive b/rpq_output_sensitive
@@ -2,4 +2,6 @@
[abokhamis2024output]: improves on [product_graph] by doing an [output_sensitive_algorithm]
+Generalizations to [CPRQ_output_sensitive] for [acyclic_CRPQs] in [abokhamis2025output]
+
Up: [rpq_query_evaluation]
diff --git a/slice b/slice
@@ -0,0 +1,9 @@
+# Slice
+
+The n-th *slice* of a [formal_language] L is the number of [words] of L having length n
+
+See also: [density_function]
+
+Up: [formal_language_theory]
+
+Aliases: n slice, k slice
