4,428 research outputs found
On Infinite Words Determined by Stack Automata
We characterize the infinite words determined by one-way stack automata. An infinite language L determines an infinite word alpha if every string in L is a prefix of alpha. If L is regular or context-free, it is known that alpha must be ultimately periodic. We extend this result to the class of languages recognized by one-way nondeterministic checking stack automata (1-NCSA). We then consider stronger classes of stack automata and show that they determine a class of infinite words which we call multilinear. We show that every multilinear word can be written in a form which is amenable to parsing. Finally, we consider the class of one-way multihead deterministic finite automata (1:multi-DFA). We show that every multilinear word can be determined by some 1:multi-DFA, but that there exist infinite words determined by 1:multi-DFA which are not multilinear
On Infinite Words Determined by Indexed Languages
We characterize the infinite words determined by indexed languages. An
infinite language determines an infinite word if every string in
is a prefix of . If is regular or context-free, it is known
that must be ultimately periodic. We show that if is an indexed
language, then is a morphic word, i.e., can be generated by
iterating a morphism under a coding. Since the other direction, that every
morphic word is determined by some indexed language, also holds, this implies
that the infinite words determined by indexed languages are exactly the morphic
words. To obtain this result, we prove a new pumping lemma for the indexed
languages, which may be of independent interest.Comment: Full version of paper accepted for publication at MFCS 201
On the Expressive Power of 2-Stack Visibly Pushdown Automata
Visibly pushdown automata are input-driven pushdown automata that recognize
some non-regular context-free languages while preserving the nice closure and
decidability properties of finite automata. Visibly pushdown automata with
multiple stacks have been considered recently by La Torre, Madhusudan, and
Parlato, who exploit the concept of visibility further to obtain a rich
automata class that can even express properties beyond the class of
context-free languages. At the same time, their automata are closed under
boolean operations, have a decidable emptiness and inclusion problem, and enjoy
a logical characterization in terms of a monadic second-order logic over words
with an additional nesting structure. These results require a restricted
version of visibly pushdown automata with multiple stacks whose behavior can be
split up into a fixed number of phases. In this paper, we consider 2-stack
visibly pushdown automata (i.e., visibly pushdown automata with two stacks) in
their unrestricted form. We show that they are expressively equivalent to the
existential fragment of monadic second-order logic. Furthermore, it turns out
that monadic second-order quantifier alternation forms an infinite hierarchy
wrt words with multiple nestings. Combining these results, we conclude that
2-stack visibly pushdown automata are not closed under complementation.
Finally, we discuss the expressive power of B\"{u}chi 2-stack visibly pushdown
automata running on infinite (nested) words. Extending the logic by an infinity
quantifier, we can likewise establish equivalence to existential monadic
second-order logic
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
Playing Games in the Baire Space
We solve a generalized version of Church's Synthesis Problem where a play is
given by a sequence of natural numbers rather than a sequence of bits; so a
play is an element of the Baire space rather than of the Cantor space. Two
players Input and Output choose natural numbers in alternation to generate a
play. We present a natural model of automata ("N-memory automata") equipped
with the parity acceptance condition, and we introduce also the corresponding
model of "N-memory transducers". We show that solvability of games specified by
N-memory automata (i.e., existence of a winning strategy for player Output) is
decidable, and that in this case an N-memory transducer can be constructed that
implements a winning strategy for player Output.Comment: In Proceedings Cassting'16/SynCoP'16, arXiv:1608.0017
Decision Problems for Deterministic Pushdown Automata on Infinite Words
The article surveys some decidability results for DPDAs on infinite words
(omega-DPDA). We summarize some recent results on the decidability of the
regularity and the equivalence problem for the class of weak omega-DPDAs.
Furthermore, we present some new results on the parity index problem for
omega-DPDAs. For the specification of a parity condition, the states of the
omega-DPDA are assigned priorities (natural numbers), and a run is accepting if
the highest priority that appears infinitely often during a run is even. The
basic simplification question asks whether one can determine the minimal number
of priorities that are needed to accept the language of a given omega-DPDA. We
provide some decidability results on variations of this question for some
classes of omega-DPDAs.Comment: In Proceedings AFL 2014, arXiv:1405.527
Event-Clock Nested Automata
In this paper we introduce and study Event-Clock Nested Automata (ECNA), a
formalism that combines Event Clock Automata (ECA) and Visibly Pushdown
Automata (VPA). ECNA allow to express real-time properties over non-regular
patterns of recursive programs. We prove that ECNA retain the same closure and
decidability properties of ECA and VPA being closed under Boolean operations
and having a decidable language-inclusion problem. In particular, we prove that
emptiness, universality, and language-inclusion for ECNA are EXPTIME-complete
problems. As for the expressiveness, we have that ECNA properly extend any
previous attempt in the literature of combining ECA and VPA
Borel Ranks and Wadge Degrees of Context Free Omega Languages
We show that, from a topological point of view, considering the Borel and the
Wadge hierarchies, 1-counter B\"uchi automata have the same accepting power
than Turing machines equipped with a B\"uchi acceptance condition. In
particular, for every non null recursive ordinal alpha, there exist some
Sigma^0_alpha-complete and some Pi^0_alpha-complete omega context free
languages accepted by 1-counter B\"uchi automata, and the supremum of the set
of Borel ranks of context free omega languages is the ordinal gamma^1_2 which
is strictly greater than the first non recursive ordinal. This very surprising
result gives answers to questions of H. Lescow and W. Thomas [Logical
Specifications of Infinite Computations, In:"A Decade of Concurrency", LNCS
803, Springer, 1994, p. 583-621]
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
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