938 research outputs found
Alternating and empty alternating auxiliary stack automata
AbstractWe consider variants of alternating auxiliary stack automata and characterize their computational power when the number of alternations is bounded by a constant or unlimited. In this way we get new characterizations of NP, the polynomial hierarchy, PSpace, and bounded query classes like co-DP=NL〈NP[1]〉 and Θ2P=PNP[O(logn)], in a uniform framework
Reachability in Higher-Order-Counters
Higher-order counter automata (\HOCS) can be either seen as a restriction of
higher-order pushdown automata (\HOPS) to a unary stack alphabet, or as an
extension of counter automata to higher levels. We distinguish two principal
kinds of \HOCS: those that can test whether the topmost counter value is zero
and those which cannot.
We show that control-state reachability for level \HOCS with -test is
complete for \mbox{}-fold exponential space; leaving out the -test
leads to completeness for \mbox{}-fold exponential time. Restricting
\HOCS (without -test) to level , we prove that global (forward or
backward) reachability analysis is \PTIME-complete. This enhances the known
result for pushdown systems which are subsumed by level \HOCS without
-test.
We transfer our results to the formal language setting. Assuming that \PTIME
\subsetneq \PSPACE \subsetneq \mathbf{EXPTIME}, we apply proof ideas of
Engelfriet and conclude that the hierarchies of languages of \HOPS and of \HOCS
form strictly interleaving hierarchies. Interestingly, Engelfriet's
constructions also allow to conclude immediately that the hierarchy of
collapsible pushdown languages is strict level-by-level due to the existing
complexity results for reachability on collapsible pushdown graphs. This
answers an open question independently asked by Parys and by Kobayashi.Comment: Version with Full Proofs of a paper that appears at MFCS 201
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
New results on pushdown module checking with imperfect information
Model checking of open pushdown systems (OPD) w.r.t. standard branching
temporal logics (pushdown module checking or PMC) has been recently
investigated in the literature, both in the context of environments with
perfect and imperfect information about the system (in the last case, the
environment has only a partial view of the system's control states and stack
content). For standard CTL, PMC with imperfect information is known to be
undecidable. If the stack content is assumed to be visible, then the problem is
decidable and 2EXPTIME-complete (matching the complexity of PMC with perfect
information against CTL). The decidability status of PMC with imperfect
information against CTL restricted to the case where the depth of the stack
content is visible is open. In this paper, we show that with this restriction,
PMC with imperfect information against CTL remains undecidable. On the other
hand, we individuate an interesting subclass of OPDS with visible stack content
depth such that PMC with imperfect information against the existential fragment
of CTL is decidable and in 2EXPTIME. Moreover, we show that the program
complexity of PMC with imperfect information and visible stack content against
CTL is 2EXPTIME-complete (hence, exponentially harder than the program
complexity of PMC with perfect information, which is known to be
EXPTIME-complete).Comment: In Proceedings GandALF 2011, arXiv:1106.081
Formats of Winning Strategies for Six Types of Pushdown Games
The solution of parity games over pushdown graphs (Walukiewicz '96) was the
first step towards an effective theory of infinite-state games. It was shown
that winning strategies for pushdown games can be implemented again as pushdown
automata. We continue this study and investigate the connection between game
presentations and winning strategies in altogether six cases of game arenas,
among them realtime pushdown systems, visibly pushdown systems, and counter
systems. In four cases we show by a uniform proof method that we obtain
strategies implementable by the same type of pushdown machine as given in the
game arena. We prove that for the two remaining cases this correspondence
fails. In the conclusion we address the question of an abstract criterion that
explains the results
Verification for Timed Automata extended with Unbounded Discrete Data Structures
We study decidability of verification problems for timed automata extended
with unbounded discrete data structures. More detailed, we extend timed
automata with a pushdown stack. In this way, we obtain a strong model that may
for instance be used to model real-time programs with procedure calls. It is
long known that the reachability problem for this model is decidable. The goal
of this paper is to identify subclasses of timed pushdown automata for which
the language inclusion problem and related problems are decidable
- …