diff --git a/regression/goto-instrument/data-flow1/main.c b/regression/goto-instrument/data-flow1/main.c
new file mode 100644
index 00000000000..1aecb44916d
--- /dev/null
+++ b/regression/goto-instrument/data-flow1/main.c
@@ -0,0 +1,18 @@
+int d=0;
+
+void f1()
+{
+  d=1;
+}
+
+int main()
+{
+  int x=2;
+  int y=3;
+
+  f1();
+
+  if(x && y && d)
+    return 0;
+}
+
diff --git a/regression/goto-instrument/data-flow1/test.desc b/regression/goto-instrument/data-flow1/test.desc
new file mode 100644
index 00000000000..e7413631c0f
--- /dev/null
+++ b/regression/goto-instrument/data-flow1/test.desc
@@ -0,0 +1,8 @@
+CORE
+main.c
+"--show-dependence-graph"
+^EXIT=0$
+^SIGNAL=0$
+Data dependencies: .*33.*
+--
+^warning: ignoring
diff --git a/src/analyses/ai.cpp b/src/analyses/ai.cpp
index f98a3f807ae..0e95e233e44 100644
--- a/src/analyses/ai.cpp
+++ b/src/analyses/ai.cpp
@@ -120,8 +120,7 @@ Function: ai_baset::entry_state
 
 void ai_baset::entry_state(const goto_programt &goto_program)
 {
-  // The first instruction of 'goto_program' is the entry point,
-  // and we make that 'top'.
+  // The first instruction of 'goto_program' is the entry point
   get_state(goto_program.instructions.begin()).make_entry();
 }
 
@@ -226,9 +225,11 @@ bool ai_baset::fixedpoint(
 {
   working_sett working_set;
 
-  // We will put all locations at least once into the working set.
-  forall_goto_program_instructions(i_it, goto_program)
-    put_in_working_set(working_set, i_it);
+  // Put the first location in the working set
+  if(!goto_program.empty())
+    put_in_working_set(
+      working_set,
+      goto_program.instructions.begin());
 
   bool new_data=false;
 
diff --git a/src/analyses/custom_bitvector_analysis.cpp b/src/analyses/custom_bitvector_analysis.cpp
index 883ea1ef188..878a7037320 100644
--- a/src/analyses/custom_bitvector_analysis.cpp
+++ b/src/analyses/custom_bitvector_analysis.cpp
@@ -326,6 +326,8 @@ void custom_bitvector_domaint::transform(
   ai_baset &ai,
   const namespacet &ns)
 {
+  if(has_values.is_false()) return;
+
   // upcast of ai
   custom_bitvector_analysist &cba=
     static_cast<custom_bitvector_analysist &>(ai);
@@ -565,8 +567,11 @@ void custom_bitvector_domaint::output(
   const ai_baset &ai,
   const namespacet &ns) const
 {
-  if(is_bottom)
-    out << "BOTTOM\n";
+  if(has_values.is_known())
+  {
+    out << has_values.to_string() << '\n';
+    return;
+  }
 
   const custom_bitvector_analysist &cba=
     static_cast<const custom_bitvector_analysist &>(ai);
@@ -625,10 +630,10 @@ bool custom_bitvector_domaint::merge(
   locationt from,
   locationt to)
 {
-  if(b.is_bottom)
+  if(b.has_values.is_false())
     return false; // no change
 
-  if(is_bottom)
+  if(has_values.is_false())
   {
     *this=b;
     return true; // change
@@ -858,7 +863,7 @@ void custom_bitvector_analysist::check(
         if(!custom_bitvector_domaint::has_get_must_or_may(i_it->guard))
           continue;
 
-        if(operator[](i_it).is_bottom) continue;
+        if(operator[](i_it).has_values.is_false()) continue;
 
         exprt tmp=eval(i_it->guard, i_it);
         result=simplify_expr(tmp, ns);
diff --git a/src/analyses/custom_bitvector_analysis.h b/src/analyses/custom_bitvector_analysis.h
index d964f34f3ec..3cdf0895ddb 100644
--- a/src/analyses/custom_bitvector_analysis.h
+++ b/src/analyses/custom_bitvector_analysis.h
@@ -10,6 +10,7 @@ Author: Daniel Kroening, kroening@kroening.com
 #define CPROVER_ANALYSES_CUSTOM_BITVECTOR_ANALYSIS_H
 
 #include <util/numbering.h>
+#include <util/threeval.h>
 
 #include "ai.h"
 #include "local_may_alias.h"
@@ -42,20 +43,19 @@ class custom_bitvector_domaint:public ai_domain_baset
   {
     may_bits.clear();
     must_bits.clear();
-    is_bottom=true;
+    has_values=tvt(false);
   }
 
   void make_top() final override
   {
-    // We don't have a proper top, and refuse to do this.
-    assert(false);
+    may_bits.clear();
+    must_bits.clear();
+    has_values=tvt(true);
   }
 
   void make_entry() final override
   {
-    may_bits.clear();
-    must_bits.clear();
-    is_bottom=false;
+    make_top();
   }
 
   bool merge(
@@ -90,9 +90,9 @@ class custom_bitvector_domaint:public ai_domain_baset
   vectorst get_rhs(const exprt &) const;
   vectorst get_rhs(const irep_idt &) const;
 
-  bool is_bottom;
+  tvt has_values;
 
-  custom_bitvector_domaint():is_bottom(true)
+  custom_bitvector_domaint():has_values(true)
   {
   }
 
diff --git a/src/analyses/dependence_graph.cpp b/src/analyses/dependence_graph.cpp
index c5ff3153ca5..0114058e0dc 100644
--- a/src/analyses/dependence_graph.cpp
+++ b/src/analyses/dependence_graph.cpp
@@ -32,7 +32,8 @@ bool dep_graph_domaint::merge(
   goto_programt::const_targett from,
   goto_programt::const_targett to)
 {
-  bool change=false;
+  bool changed=has_values.is_false();
+  has_values=tvt::unknown();
 
   depst::iterator it=control_deps.begin();
   for(depst::const_iterator ito=src.control_deps.begin();
@@ -44,7 +45,7 @@ bool dep_graph_domaint::merge(
     if(it==control_deps.end() || *ito<*it)
     {
       control_deps.insert(it, *ito);
-      change=true;
+      changed=true;
     }
     else if(it!=control_deps.end())
       ++it;
@@ -60,13 +61,13 @@ bool dep_graph_domaint::merge(
     if(it==data_deps.end() || *ito<*it)
     {
       data_deps.insert(it, *ito);
-      change=true;
+      changed=true;
     }
     else if(it!=data_deps.end())
       ++it;
   }
 
-  return change;
+  return changed;
 }
 
 /*******************************************************************\
diff --git a/src/analyses/dependence_graph.h b/src/analyses/dependence_graph.h
index e783fae8fda..15c0828fef6 100644
--- a/src/analyses/dependence_graph.h
+++ b/src/analyses/dependence_graph.h
@@ -13,6 +13,7 @@ Date: August 2013
 #define CPROVER_ANALYSES_DEPENDENCE_GRAPH_H
 
 #include <util/graph.h>
+#include <util/threeval.h>
 
 #include "ai.h"
 #include "cfg_dominators.h"
@@ -70,6 +71,7 @@ class dep_graph_domaint:public ai_domain_baset
   typedef graph<dep_nodet>::node_indext node_indext;
 
   dep_graph_domaint():
+    has_values(false),
     node_id(std::numeric_limits<node_indext>::max())
   {
   }
@@ -89,20 +91,22 @@ class dep_graph_domaint:public ai_domain_baset
     std::ostream &out,
     const ai_baset &ai,
     const namespacet &ns) const final override;
-    
+
   void make_top() final override
   {
+    has_values=tvt(true);
     node_id=std::numeric_limits<node_indext>::max();
   }
 
   void make_bottom() final override
   {
+    has_values=tvt(false);
     node_id=std::numeric_limits<node_indext>::max();
   }
 
   void make_entry() final override
   {
-    node_id=std::numeric_limits<node_indext>::max();
+    make_top();
   }
 
   void set_node_id(node_indext id)
@@ -117,6 +121,7 @@ class dep_graph_domaint:public ai_domain_baset
   }
 
 protected:
+  tvt has_values;
   node_indext node_id;
 
   typedef std::set<goto_programt::const_targett> depst;
diff --git a/src/analyses/escape_analysis.cpp b/src/analyses/escape_analysis.cpp
index 7d610c3198a..711dd35d170 100644
--- a/src/analyses/escape_analysis.cpp
+++ b/src/analyses/escape_analysis.cpp
@@ -266,6 +266,8 @@ void escape_domaint::transform(
   ai_baset &ai,
   const namespacet &ns)
 {
+  if(has_values.is_false()) return;
+
   // upcast of ai
   //escape_analysist &ea=
   //  static_cast<escape_analysist &>(ai);
@@ -364,9 +366,9 @@ void escape_domaint::output(
   const ai_baset &ai,
   const namespacet &ns) const
 {
-  if(is_bottom)
+  if(has_values.is_known())
   {
-    out << "BOTTOM\n";
+    out << has_values.to_string() << '\n';
     return;
   }
 
@@ -422,10 +424,10 @@ bool escape_domaint::merge(
   locationt from,
   locationt to)
 {
-  if(b.is_bottom)
+  if(b.has_values.is_false())
     return false; // no change
 
-  if(is_bottom)
+  if(has_values.is_false())
   {
     *this=b;
     return true; // change
diff --git a/src/analyses/escape_analysis.h b/src/analyses/escape_analysis.h
index c485a01140e..3cccec91a30 100644
--- a/src/analyses/escape_analysis.h
+++ b/src/analyses/escape_analysis.h
@@ -11,6 +11,7 @@ Author: Daniel Kroening, kroening@kroening.com
 #define CPROVER_ANALYSES_ESCAPE_ANALYSIS_H
 
 #include <util/numbering.h>
+#include <util/threeval.h>
 #include <util/union_find.h>
 
 #include "ai.h"
@@ -28,7 +29,7 @@ class escape_analysist;
 class escape_domaint:public ai_domain_baset
 {
 public:
-  escape_domaint():is_bottom(true)
+  escape_domaint():has_values(false)
   {
   }
 
@@ -51,19 +52,20 @@ class escape_domaint:public ai_domain_baset
   void make_bottom() override final
   {
     cleanup_map.clear();
-    is_bottom=true;
+    aliases.clear();
+    has_values=tvt(false);
   }
 
   void make_top() override final
   {
-    // We don't have a proper top.
-    assert(false);
+    cleanup_map.clear();
+    aliases.clear();
+    has_values=tvt(true);
   }
-  
+
   void make_entry() override final
   {
-    cleanup_map.clear();
-    is_bottom=false;
+    make_top();
   }
 
   typedef union_find<irep_idt> aliasest;
@@ -80,9 +82,9 @@ class escape_domaint:public ai_domain_baset
   typedef std::map<irep_idt, cleanupt > cleanup_mapt;
   cleanup_mapt cleanup_map;
 
-  bool is_bottom;
-
 protected:
+  tvt has_values;
+
   void assign_lhs_cleanup(const exprt &, const std::set<irep_idt> &);
   void get_rhs_cleanup(const exprt &, std::set<irep_idt> &);
   void assign_lhs_aliases(const exprt &, const std::set<irep_idt> &);
diff --git a/src/analyses/global_may_alias.cpp b/src/analyses/global_may_alias.cpp
index 0e3e190aa29..f89530d3ed8 100644
--- a/src/analyses/global_may_alias.cpp
+++ b/src/analyses/global_may_alias.cpp
@@ -130,6 +130,8 @@ void global_may_alias_domaint::transform(
   ai_baset &ai,
   const namespacet &ns)
 {
+  if(has_values.is_false()) return;
+
   const goto_programt::instructiont &instruction=*from;
 
   switch(instruction.type)
@@ -179,6 +181,12 @@ void global_may_alias_domaint::output(
   const ai_baset &ai,
   const namespacet &ns) const
 {
+  if(has_values.is_known())
+  {
+    out << has_values.to_string() << '\n';
+    return;
+  }
+
   for(aliasest::const_iterator a_it1=aliases.begin();
       a_it1!=aliases.end();
       a_it1++)
@@ -218,7 +226,8 @@ bool global_may_alias_domaint::merge(
   locationt from,
   locationt to)
 {
-  bool changed=false;
+  bool changed=has_values.is_false();
+  has_values=tvt::unknown();
 
   // do union
   for(aliasest::const_iterator it=b.aliases.begin();
diff --git a/src/analyses/global_may_alias.h b/src/analyses/global_may_alias.h
index 0b4d178baab..69eaa22404b 100644
--- a/src/analyses/global_may_alias.h
+++ b/src/analyses/global_may_alias.h
@@ -11,6 +11,7 @@ Author: Daniel Kroening, kroening@kroening.com
 #define CPROVER_ANALYSES_GLOBAL_MAY_ALIAS_H
 
 #include <util/numbering.h>
+#include <util/threeval.h>
 #include <util/union_find.h>
 
 #include "ai.h"
@@ -28,6 +29,10 @@ class global_may_alias_analysist;
 class global_may_alias_domaint:public ai_domain_baset
 {
 public:
+  global_may_alias_domaint():has_values(false)
+  {
+  }
+
   void transform(
     locationt from,
     locationt to,
@@ -47,23 +52,26 @@ class global_may_alias_domaint:public ai_domain_baset
   void make_bottom() final override
   {
     aliases.clear();
+    has_values=tvt(false);
   }
 
   void make_top() final override
   {
-    // We don't have a proper top.
-    assert(false);
+    aliases.clear();
+    has_values=tvt(true);
   }
 
   void make_entry() final override
   {
-    aliases.clear();
+    make_top();
   }
 
   typedef union_find<irep_idt> aliasest;
   aliasest aliases;
 
 protected:
+  tvt has_values;
+
   void assign_lhs_aliases(const exprt &, const std::set<irep_idt> &);
   void get_rhs_aliases(const exprt &, std::set<irep_idt> &);
   void get_rhs_aliases_address_of(const exprt &, std::set<irep_idt> &);
diff --git a/src/analyses/invariant_set_domain.h b/src/analyses/invariant_set_domain.h
index 2190b0503b4..99923f536f9 100644
--- a/src/analyses/invariant_set_domain.h
+++ b/src/analyses/invariant_set_domain.h
@@ -9,12 +9,19 @@ Author: Daniel Kroening, kroening@kroening.com
 #ifndef CPROVER_ANALYSES_INVARIANT_SET_DOMAIN_H
 #define CPROVER_ANALYSES_INVARIANT_SET_DOMAIN_H
 
+#include <util/threeval.h>
+
 #include "ai.h"
 #include "invariant_set.h"
 
 class invariant_set_domaint:public ai_domain_baset
 {
 public:
+  invariant_set_domaint():has_values(false)
+  {
+  }
+
+  tvt has_values;
   invariant_sett invariant_set;
 
   // overloading
@@ -24,7 +31,11 @@ class invariant_set_domaint:public ai_domain_baset
     locationt from,
     locationt to)
   {
-    return invariant_set.make_union(other.invariant_set);
+    bool changed=invariant_set.make_union(other.invariant_set) ||
+                 has_values.is_false();
+    has_values=tvt::unknown();
+
+    return changed;
   }
 
   void output(
@@ -32,7 +43,10 @@ class invariant_set_domaint:public ai_domain_baset
     const ai_baset &ai,
     const namespacet &ns) const override final
   {
-    invariant_set.output("", out);
+    if(has_values.is_known())
+      out << has_values.to_string() << '\n';
+    else
+      invariant_set.output("", out);
   }
 
   virtual void transform(
@@ -40,20 +54,23 @@ class invariant_set_domaint:public ai_domain_baset
     locationt to_l,
     ai_baset &ai,
     const namespacet &ns) override final;
-    
+
   void make_top() override final
   {
     invariant_set.make_true();
+    has_values=tvt(true);
   }
 
   void make_bottom() override final
   {
     invariant_set.make_false();
+    has_values=tvt(false);
   }
 
   void make_entry() override final
   {
     invariant_set.make_true();
+    has_values=tvt(true);
   }
 };
 
diff --git a/src/analyses/is_threaded.cpp b/src/analyses/is_threaded.cpp
index 0b3df79a553..1c14ad9d424 100644
--- a/src/analyses/is_threaded.cpp
+++ b/src/analyses/is_threaded.cpp
@@ -34,7 +34,7 @@ class is_threaded_domaint:public ai_domain_baset
     bool old_reachable=reachable;
     if(src.reachable)
       reachable=true;
-  
+
     bool old_h_s=has_spawn;
     if(src.has_spawn &&
        (from->is_end_function() ||
@@ -66,7 +66,7 @@ class is_threaded_domaint:public ai_domain_baset
       is_threaded=true;
     }
   }
-  
+
   void make_bottom() override final
   {
     reachable=has_spawn=is_threaded=false;
@@ -76,7 +76,7 @@ class is_threaded_domaint:public ai_domain_baset
   {
     reachable=has_spawn=is_threaded=true;
   }
-  
+
   void make_entry() override final
   {
     reachable=true;
diff --git a/src/analyses/reaching_definitions.cpp b/src/analyses/reaching_definitions.cpp
index c0cda391b9e..04809464c70 100644
--- a/src/analyses/reaching_definitions.cpp
+++ b/src/analyses/reaching_definitions.cpp
@@ -679,6 +679,13 @@ Function: rd_range_domaint::output
 void rd_range_domaint::output(std::ostream &out) const
 {
   out << "Reaching definitions:" << std::endl;
+
+  if(has_values.is_known())
+  {
+    out << has_values.to_string() << '\n';
+    return;
+  }
+
   for(valuest::const_iterator
       it=values.begin();
       it!=values.end();
@@ -797,7 +804,8 @@ bool rd_range_domaint::merge(
   locationt from,
   locationt to)
 {
-  bool more=false;
+  bool changed=has_values.is_false();
+  has_values=tvt::unknown();
 
   valuest::iterator it=values.begin();
   for(valuest::const_iterator ito=other.values.begin();
@@ -809,7 +817,7 @@ bool rd_range_domaint::merge(
     if(it==values.end() || ito->first<it->first)
     {
       values.insert(*ito);
-      more=true;
+      changed=true;
     }
     else if(it!=values.end())
     {
@@ -817,7 +825,7 @@ bool rd_range_domaint::merge(
 
       if(merge_inner(it->second, ito->second))
       {
-        more=true;
+        changed=true;
         export_cache.erase(it->first);
       }
 
@@ -825,7 +833,7 @@ bool rd_range_domaint::merge(
     }
   }
 
-  return more;
+  return changed;
 }
 
 /*******************************************************************\
@@ -853,7 +861,8 @@ bool rd_range_domaint::merge_shared(
   assert(rd!=0);
 #endif
 
-  bool more=false;
+  bool changed=has_values.is_false();
+  has_values=tvt::unknown();
 
   valuest::iterator it=values.begin();
   for(valuest::const_iterator ito=other.values.begin();
@@ -871,7 +880,7 @@ bool rd_range_domaint::merge_shared(
     if(it==values.end() || ito->first<it->first)
     {
       values.insert(*ito);
-      more=true;
+      changed=true;
     }
     else if(it!=values.end())
     {
@@ -879,7 +888,7 @@ bool rd_range_domaint::merge_shared(
 
       if(merge_inner(it->second, ito->second))
       {
-        more=true;
+        changed=true;
         export_cache.erase(it->first);
       }
 
@@ -887,7 +896,7 @@ bool rd_range_domaint::merge_shared(
     }
   }
 
-  return more;
+  return changed;
 }
 
 /*******************************************************************\
diff --git a/src/analyses/reaching_definitions.h b/src/analyses/reaching_definitions.h
index 0d1d2e36f39..a047e5cd782 100644
--- a/src/analyses/reaching_definitions.h
+++ b/src/analyses/reaching_definitions.h
@@ -12,6 +12,8 @@ Date: February 2013
 #ifndef CPROVER_ANALYSES_REACHING_DEFINITIONS_H
 #define CPROVER_ANALYSES_REACHING_DEFINITIONS_H
 
+#include <util/threeval.h>
+
 #include "ai.h"
 #include "goto_rw.h"
 
@@ -44,6 +46,12 @@ class sparse_bitvector_analysist
     return entry.first->second;
   }
 
+  void clear()
+  {
+    value_map.clear();
+    values.clear();
+  }
+
 protected:
   typedef typename std::map<V, std::size_t> inner_mapt;
   std::vector<typename inner_mapt::const_iterator> values;
@@ -83,6 +91,7 @@ class rd_range_domaint:public ai_domain_baset
 public:
   rd_range_domaint():
     ai_domain_baset(),
+    has_values(false),
     bv_container(0)
   {
   }
@@ -106,20 +115,24 @@ class rd_range_domaint:public ai_domain_baset
   {
     output(out);
   }
-  
+
   void make_top() override final
   {
     values.clear();
+    if(bv_container) bv_container->clear();
+    has_values=tvt(true);
   }
 
   void make_bottom() override final
   {
     values.clear();
+    if(bv_container) bv_container->clear();
+    has_values=tvt(false);
   }
 
   void make_entry() override final
   {
-    values.clear();
+    make_top();
   }
 
   // returns true iff there is s.th. new
@@ -145,6 +158,8 @@ class rd_range_domaint:public ai_domain_baset
   }
 
 protected:
+  tvt has_values;
+
   sparse_bitvector_analysist<reaching_definitiont> *bv_container;
 
   typedef std::set<std::size_t> values_innert;
diff --git a/src/analyses/uninitialized_domain.cpp b/src/analyses/uninitialized_domain.cpp
index e0aa7b0c057..36640250fa8 100644
--- a/src/analyses/uninitialized_domain.cpp
+++ b/src/analyses/uninitialized_domain.cpp
@@ -31,7 +31,7 @@ void uninitialized_domaint::transform(
   ai_baset &ai,
   const namespacet &ns)
 {
-  if(is_bottom) return;
+  if(has_values.is_false()) return;
 
   switch(from->type)
   {
@@ -98,8 +98,8 @@ void uninitialized_domaint::output(
   const ai_baset &ai,
   const namespacet &ns) const
 {
-  if(is_bottom)
-    out << "BOTTOM";
+  if(has_values.is_known())
+    out << has_values.to_string() << '\n';
   else
   {
     for(const auto & id : uninitialized)
@@ -124,16 +124,16 @@ bool uninitialized_domaint::merge(
   locationt from,
   locationt to)
 {
-  bool old_is_bottom=is_bottom;
-  
-  is_bottom=is_bottom && other.is_bottom;
-  
   unsigned old_uninitialized=uninitialized.size();
 
   uninitialized.insert(
     other.uninitialized.begin(),
     other.uninitialized.end());
 
-  return old_is_bottom!=is_bottom ||
-         old_uninitialized!=uninitialized.size();
+  bool changed=
+    (has_values.is_false() && !other.has_values.is_false()) ||
+    old_uninitialized!=uninitialized.size();
+  has_values=tvt::unknown();
+
+  return changed;
 }
diff --git a/src/analyses/uninitialized_domain.h b/src/analyses/uninitialized_domain.h
index 89943ef8054..93f1f2fd2b8 100644
--- a/src/analyses/uninitialized_domain.h
+++ b/src/analyses/uninitialized_domain.h
@@ -11,16 +11,16 @@ Date: January 2010
 #ifndef CPROVER_ANALYSES_UNINITIALIZED_DOMAIN_H
 #define CPROVER_ANALYSES_UNINITIALIZED_DOMAIN_H
 
+#include <util/threeval.h>
+
 #include "ai.h"
 
 class uninitialized_domaint:public ai_domain_baset
 {
 public:
-  uninitialized_domaint():is_bottom(true)
+  uninitialized_domaint():has_values(false)
   {
   }
-  
-  bool is_bottom;
 
   // Locals that are declared but may not be initialized
   typedef std::set<irep_idt> uninitializedt;
@@ -36,17 +36,17 @@ class uninitialized_domaint:public ai_domain_baset
     std::ostream &out,
     const ai_baset &ai,
     const namespacet &ns) const override final;
-    
+
   void make_top() override final
   {
-    // We don't have a proper 'top', and refuse to do this.
-    assert(false);
+    uninitialized.clear();
+    has_values=tvt(true);
   }
 
   void make_bottom() override final
   {
     uninitialized.clear();
-    is_bottom=true;
+    has_values=tvt(false);
   }
 
   void make_entry() override final
@@ -61,6 +61,8 @@ class uninitialized_domaint:public ai_domain_baset
     locationt to);
 
 protected:
+  tvt has_values;
+
   void assign(const exprt &lhs);
 };