First cut at introducing fsm_intersect_charset(), exposed as fsm -U.

include/fsm/bool.h

@@ -55,6 +55,14 @@ fsm_union_array(size_t fsm_count,
 struct fsm *
 fsm_intersect(struct fsm *a, struct fsm *b);
 
+/*
+ * A convenience to intersect against a character set, rather than
+ * a pre-existing FSM. Unlike fsm_intersect(), the FSM is required
+ * to be a DFA.
+ */
+struct fsm *
+fsm_intersect_charset(struct fsm *a, size_t n, const char *charset);
+
 /*
  * Subtract b from a. This is not commutative.
  */

man/fsm.1/fsm.1.xml

@@ -22,6 +22,7 @@
 	<!ENTITY io.arg "<replaceable>io</replaceable>">
 	<!ENTITY iterations.arg "<replaceable>iterations</replaceable>">
 	<!ENTITY length.arg "<replaceable>length</replaceable>">
+	<!ENTITY charset.arg "<replaceable>charset</replaceable>">
 
 	<!ENTITY a.opt "<option>-a</option>">
 	<!ENTITY w.opt "<option>-w</option>">
@@ -32,6 +33,7 @@
 	<!ENTITY G.opt "<option>-G</option>&nbsp;&length.arg;">
 	<!ENTITY k.opt "<option>-k</option>&nbsp;&io.arg;">
 	<!ENTITY i.opt "<option>-i</option>&nbsp;&iterations.arg;">
+	<!ENTITY U.opt "<option>-U</option>&nbsp;&charset.arg;">
 	<!ENTITY X.opt "<option>-X</option>">
 
 	<!ENTITY d.opt "<option>-d</option>">
@@ -75,6 +77,7 @@
 			<command>fsm</command>
 
 			<arg choice="opt">&x.opt;</arg>
+			<arg choice="opt">&U.opt;</arg>
 
 			<arg choice="plain" rep="repeat">&str.arg;</arg>
 		</cmdsynopsis>
@@ -83,6 +86,7 @@
 			<command>fsm</command>
 
 			<arg choice="plain">&p.opt;</arg>
+			<arg choice="opt">&U.opt;</arg>
 
 			<arg choice="opt">&l.opt;</arg>
 			<arg choice="opt">&a.opt;</arg>
@@ -103,6 +107,7 @@
 				<arg choice="plain">&r.opt;</arg>
 				<arg choice="plain">&t.opt;</arg>
 			</group>
+			<arg choice="opt">&U.opt;</arg>
 
 			<arg choice="opt">&i.opt;</arg>
 		</cmdsynopsis>
@@ -111,6 +116,7 @@
 			<command>fsm</command>
 
 			<arg choice="req" rep="repeat">&q.opt;</arg>
+			<arg choice="opt">&U.opt;</arg>
 
 			<arg choice="plain" rep="repeat">&file.arg;</arg>
 		</cmdsynopsis>
@@ -190,6 +196,21 @@
 				</listitem>
 			</varlistentry>
 
+			<varlistentry>
+				<term>&U.opt;</term>
+
+				<listitem>
+					<para>Intersect the resulting state machine down to a
+						given character set.
+						This is done after any transformations are applied
+						(e.g. by <option>t</option>).</para>
+
+					<para>The default character set is a byte.
+						It is not possible to specify a particular character set
+						that includes a literal <literal>\0</literal>.</para>
+				</listitem>
+			</varlistentry>
+
 			<varlistentry>
 				<term>&w.opt;</term>
 

src/fsm/main.c

@@ -368,6 +368,7 @@ main(int argc, char *argv[])
 	double elapsed;
 	fsm_print *print;
 	enum op op;
+	const char *charset;
 	struct fsm *fsm;
 	int xfiles;
 	int r;
@@ -395,7 +396,7 @@ main(int argc, char *argv[])
 	{
 		int c;
 
-		while (c = getopt(argc, argv, "h" "aCcgwXe:k:i:" "xpq:l:dG:mrt:EW:"), c != -1) {
+		while (c = getopt(argc, argv, "h" "aCcgwXe:k:i:" "xpq:l:dG:mrt:EU:W:"), c != -1) {
 			switch (c) {
 			case 'a': opt.anonymous_states  = 1;          break;
 			case 'c': opt.consolidate_edges = 1;          break;
@@ -421,13 +422,19 @@ main(int argc, char *argv[])
 			case 'r': op = op_name("reverse");            break;
 			case 't': op = op_name(optarg);               break;
 			case 'E': op = op_name("remove_epsilons");    break;
+
+			case 'U':
+				charset = optarg;
+				break;
+
 			case 'W':
 				/* print = gen_words; */
 				/* num_words = strtoul(optarg, NULL, 10); */
 				/* XXX: error handling */
 				fprintf(stderr, "not yet implemented.\n");
 				exit(EXIT_FAILURE);
 				break;
+
 			case 'G':
 				generate_bounds = strtoul(optarg, NULL, 10);
 				if (generate_bounds == 0) {
@@ -548,6 +555,29 @@ main(int argc, char *argv[])
 			q = NULL;
 		}
 
+		/*
+		 * It might be more efficient to intersect the character set for each
+		 * operand, but that gives a different result for some operations
+		 * (complement especially). So since we'd also need to intersect the
+		 * result here too, I'm just doing it in the one place for simplicity.
+		 *
+		 * Passing a NULL charset is a no-op, so the default charset is a byte.
+		 * We can't include \0 here because optarg is a string, and I don't
+		 * want to invent a syntax for character sets.
+		 */
+		if (charset != NULL) {
+			if (!fsm_determinise(q)) {
+				perror("fsm_determinise");
+				exit(EXIT_FAILURE);
+			}
+
+			q = fsm_intersect_charset(q, strlen(charset), charset);
+			if (q == NULL) {
+				perror("fsm_intersect_charset");
+				exit(EXIT_FAILURE);
+			}
+		}
+
 		fsm_to_cleanup = q;
 
 		if (-1 == clock_gettime(CLOCK_MONOTONIC, &post)) {

src/libfsm/Makefile

@@ -1,6 +1,7 @@
 .include "../../share/mk/top.mk"
 
 SRC += src/libfsm/capture.c
+SRC += src/libfsm/charset.c
 SRC += src/libfsm/collate.c
 SRC += src/libfsm/complete.c
 SRC += src/libfsm/consolidate.c

src/libfsm/charset.c

@@ -0,0 +1,95 @@
+/*
+ * Copyright 2024 Katherine Flavel
+ *
+ * See LICENCE for the full copyright terms.
+ */
+
+#include <assert.h>
+#include <stdbool.h>
+#include <stddef.h>
+
+#include <fsm/fsm.h>
+#include <fsm/bool.h>
+#include <fsm/pred.h>
+#include <fsm/walk.h>
+
+#include "internal.h"
+#include "walk2.h"
+
+/* ^[abc..]*$ */
+struct fsm *
+fsm_intersect_charset(struct fsm *a, size_t n, const char *charset)
+{
+	struct fsm *b, *q;
+
+	assert(a != NULL);
+
+	if (charset == NULL) {
+		return a;
+	}
+
+	/*
+	 * Since intersection is destructive, there's no point in making
+	 * the charset FSM in advance and then fsm_clone()ing it.
+	 * We may as well just make a new one each time.
+	 */
+	{
+		fsm_state_t state;
+
+		// TODO: pass .statealloc explicitly, we know it's 1. the default is overkill
+		b = fsm_new(a->opt);
+		if (b == NULL) {
+			return NULL;
+		}
+
+		if (!fsm_addstate(b, &state)) {
+			goto error;
+		}
+
+		for (size_t i = 0; i < n; i++) {
+			if (!fsm_addedge_literal(b, state, state, charset[i])) {
+				goto error;
+			}
+		}
+
+		fsm_setend(b, state, true);
+		fsm_setstart(b, state);
+	}
+
+// TODO: document prerequisites
+	assert(fsm_all(a, fsm_isdfa));
+	assert(fsm_all(b, fsm_isdfa));
+
+	/*
+	 * This is equivalent to fsm_intersect(). fsm_intersect() asserts that
+	 * both operands are DFA at runtime. But we know this empirically from
+	 * our callers. So we call fsm_walk2() directly to avoid needlessly
+	 * running the DFA predicate in DNDEBUG builds.
+	 *
+	 * This is intersection implemented by walking sets of states through
+	 * both FSM simultaneously, as described by Hopcroft, Motwani and Ullman
+	 * (2001, 2nd ed.) 4.2, Closure under Intersection.
+	 *
+	 * The intersection of two FSM consists of only those items which
+	 * are present in _BOTH.
+	 */
+	q = fsm_walk2(a, b, FSM_WALK2_BOTH, FSM_WALK2_BOTH);
+	if (q == NULL) {
+		return NULL;
+	}
+
+	fsm_free(a);
+	fsm_free(b);
+
+	/* walking two DFA produces a DFA */
+	assert(fsm_all(q, fsm_isdfa));
+
+	return q;
+
+error:
+
+	fsm_free(b);
+
+	return NULL;
+}
+

src/libfsm/libfsm.syms

@@ -3,6 +3,7 @@ fsm_complement
 fsm_union
 fsm_union_array
 fsm_intersect
+fsm_intersect_charset
 
 # <fsm/cost.h>
 fsm_cost_legible