953 research outputs found
Visibly Linear Dynamic Logic
We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear
Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown
languages over finite words. In VLDL one can, e.g., express that a function
resets a variable to its original value after its execution, even in the
presence of an unbounded number of intermediate recursive calls. We prove that
VLDL describes exactly the -visibly pushdown languages. Thus it is
strictly more expressive than LTL and able to express recursive properties of
programs with unbounded call stacks.
The main technical contribution of this work is a translation of VLDL into
-visibly pushdown automata of exponential size via one-way alternating
jumping automata. This translation yields exponential-time algorithms for
satisfiability, validity, and model checking. We also show that visibly
pushdown games with VLDL winning conditions are solvable in triply-exponential
time. We prove all these problems to be complete for their respective
complexity classes.Comment: 25 Page
Streamability of nested word transductions
We consider the problem of evaluating in streaming (i.e., in a single
left-to-right pass) a nested word transduction with a limited amount of memory.
A transduction T is said to be height bounded memory (HBM) if it can be
evaluated with a memory that depends only on the size of T and on the height of
the input word. We show that it is decidable in coNPTime for a nested word
transduction defined by a visibly pushdown transducer (VPT), if it is HBM. In
this case, the required amount of memory may depend exponentially on the height
of the word. We exhibit a sufficient, decidable condition for a VPT to be
evaluated with a memory that depends quadratically on the height of the word.
This condition defines a class of transductions that strictly contains all
determinizable VPTs
Revisiting Underapproximate Reachability for Multipushdown Systems
Boolean programs with multiple recursive threads can be captured as pushdown
automata with multiple stacks. This model is Turing complete, and hence, one is
often interested in analyzing a restricted class that still captures useful
behaviors. In this paper, we propose a new class of bounded under
approximations for multi-pushdown systems, which subsumes most existing
classes. We develop an efficient algorithm for solving the under-approximate
reachability problem, which is based on efficient fix-point computations. We
implement it in our tool BHIM and illustrate its applicability by generating a
set of relevant benchmarks and examining its performance. As an additional
takeaway, BHIM solves the binary reachability problem in pushdown automata. To
show the versatility of our approach, we then extend our algorithm to the timed
setting and provide the first implementation that can handle timed
multi-pushdown automata with closed guards.Comment: 52 pages, Conference TACAS 202
Rigid Tree Automata and Applications
International audienceWe introduce the class of Rigid Tree Automata (RTA), an extension of standard bottom-up automata on ranked trees with distinguished states called rigid. Rigid states define a restriction on the computation of RTA on trees: RTA can test for equality in subtrees reaching the same rigid state. RTA are able to perform local and global tests of equality between subtrees, non-linear tree pattern matching, and some inequality and disequality tests as well. Properties like determinism, pumping lemma, Boolean closure, and several decision problems are studied in detail. In particular, the emptiness problem is shown decidable in linear time for RTA whereas membership of a given tree to the language of a given RTA is NP-complete. Our main result is the decidability of whether a given tree belongs to the rewrite closure of an RTA language under a restricted family of term rewriting systems, whereas this closure is not an RTA language. This result, one of the first on rewrite closure of languages of tree automata with constraints, is enabling the extension of model checking procedures based on finite tree automata techniques, in particular for the verification of communicating processes with several local non rewritable memories, like security protocols. Finally, a comparison of RTA with several classes of tree automata with local and global equality tests, with dag automata and Horn clause formalisms is also provided
Generalizing input-driven languages: theoretical and practical benefits
Regular languages (RL) are the simplest family in Chomsky's hierarchy. Thanks
to their simplicity they enjoy various nice algebraic and logic properties that
have been successfully exploited in many application fields. Practically all of
their related problems are decidable, so that they support automatic
verification algorithms. Also, they can be recognized in real-time.
Context-free languages (CFL) are another major family well-suited to
formalize programming, natural, and many other classes of languages; their
increased generative power w.r.t. RL, however, causes the loss of several
closure properties and of the decidability of important problems; furthermore
they need complex parsing algorithms. Thus, various subclasses thereof have
been defined with different goals, spanning from efficient, deterministic
parsing to closure properties, logic characterization and automatic
verification techniques.
Among CFL subclasses, so-called structured ones, i.e., those where the
typical tree-structure is visible in the sentences, exhibit many of the
algebraic and logic properties of RL, whereas deterministic CFL have been
thoroughly exploited in compiler construction and other application fields.
After surveying and comparing the main properties of those various language
families, we go back to operator precedence languages (OPL), an old family
through which R. Floyd pioneered deterministic parsing, and we show that they
offer unexpected properties in two fields so far investigated in totally
independent ways: they enable parsing parallelization in a more effective way
than traditional sequential parsers, and exhibit the same algebraic and logic
properties so far obtained only for less expressive language families
{SAT} Solvers for Queries over Tree Automata with Constraints
International audienceTree automata turned out to be a very convenient framework for modeling and proving properties on infinite systems like communication protocols, Java programs and also in the context of XML programming. Unfortunately, these works are not always supported by efficient verification and validation tools. This paper investigates the use of two SAT solvers --- minisat and picosat--- to evaluate queries over tree automata with global equality and disequality constraints (TAGED s for short). Unlike general tree automata, TAGED s allow to express constraints useful for e.g., evaluating queries over XML documents, like "in the document, two nodes do not have the same key". These queries being based on the membership problem which is NP-complete for TAGEDs, we propose an efficient SAT encoding of the membership problem for TAGEDs and we show its correctness and soundness. The paper reports on the experimental results, and implementation details are given
The Emptiness Problem for Tree Automata with at Least One Disequality Constraint is NP-hard
The model of tree automata with equality and disequality constraints was
introduced in 2007 by Filiot, Talbot and Tison. In this paper we show that if
there is at least one disequality constraint, the emptiness problem is NP-hard
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