Deciding Conditional Termination

We address the problem of conditional termination, which is that of defining the set of initial configurations from which a given program always terminates. First we define the dual set, of initial configurations from which a non-terminating execution exists, as the greatest fixpoint of the function that maps a set of states into its pre-image with respect to the transition relation. This definition allows to compute the weakest non-termination precondition if at least one of the following holds: (i) the transition relation is deterministic, (ii) the descending Kleene sequence overapproximating the greatest fixpoint converges in finitely many steps, or (iii) the transition relation is well founded. We show that this is the case for two classes of relations, namely octagonal and finite monoid affine relations. Moreover, since the closed forms of these relations can be defined in Presburger arithmetic, we obtain the decidability of the termination problem for such loops.Comment: 61 pages, 6 figures, 2 table

Advances and applications of automata on words and trees : executive summary

Seminar: 10501 - Advances and Applications of Automata on Words and Trees. The aim of the seminar was to discuss and systematize the recent fast progress in automata theory and to identify important directions for future research. For this, the seminar brought together more than 40 researchers from automata theory and related fields of applications. We had 19 talks of 30 minutes and 5 one-hour lectures leaving ample room for discussions. In the following we describe the topics in more detail

The PER model of abstract non-interference

Abstract. In this paper, we study the relationship between two models of secure information flow: the PER model (which uses equivalence relations) and the abstract non-interference model (which uses upper closure operators). We embed the lattice of equivalence relations into the lattice of closures, re-interpreting abstract non-interference over the lattice of equivalence relations. For narrow abstract non-interference, we show non-interference it is strictly less general. The relational presentation of abstract non-interference leads to a simplified construction of the most concrete harmless attacker. Moreover, the PER model of abstract noninterference allows us to derive unconstrained attacker models, which do not necessarily either observe all public information or ignore all private information. Finally, we show how abstract domain completeness can be used for enforcing the PER model of abstract non-interference

Closures of may and must convergence for contextual equivalence

We show on an abstract level that contextual equivalence in non-deterministic program calculi defined by may- and must-convergence is maximal in the following sense. Using also all the test predicates generated by the Boolean, forall- and existential closure of may- and must-convergence does not change the contextual equivalence. The situation is different if may- and total must-convergence is used, where an expression totally must-converges if all reductions are finite and terminate with a value: There is an infinite sequence of test-predicates generated by the Boolean, forall- and existential closure of may- and total must-convergence, which also leads to an infinite sequence of different contextual equalities

Advances and applications of automata on words and trees : abstracts collection

From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 "Advances and Applications of Automata on Words and Trees" was held in Schloss Dagstuhl - Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Automata with Nested Pebbles Capture First-Order Logic with Transitive Closure

String languages recognizable in (deterministic) log-space are characterized either by two-way (deterministic) multi-head automata, or following Immerman, by first-order logic with (deterministic) transitive closure. Here we elaborate this result, and match the number of heads to the arity of the transitive closure. More precisely, first-order logic with k-ary deterministic transitive closure has the same power as deterministic automata walking on their input with k heads, additionally using a finite set of nested pebbles. This result is valid for strings, ordered trees, and in general for families of graphs having a fixed automaton that can be used to traverse the nodes of each of the graphs in the family. Other examples of such families are grids, toruses, and rectangular mazes. For nondeterministic automata, the logic is restricted to positive occurrences of transitive closure. The special case of k=1 for trees, shows that single-head deterministic tree-walking automata with nested pebbles are characterized by first-order logic with unary deterministic transitive closure. This refines our earlier result that placed these automata between first-order and monadic second-order logic on trees.Comment: Paper for Logical Methods in Computer Science, 27 pages, 1 figur