109 research outputs found
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
An optimal construction of Hanf sentences
We give the first elementary construction of equivalent formulas in Hanf
normal form. The triply exponential upper bound is complemented by a matching
lower bound
One-Counter Automata with Counter Observability
In a one-counter automaton (OCA), one can produce a letter from some finite alphabet, increment and decrement the counter by one, or compare it with constants up to some threshold. It is well-known that universality and language inclusion for OCAs are undecidable. In this paper, we consider OCAs with counter observability: Whenever the automaton produces a letter, it outputs the current counter value along with it. Hence, its language is now a set of words over an infinite alphabet. We show that universality and inclusion for that model are PSPACE-complete, thus no harder than the corresponding problems for finite automata. In fact, by establishing a link with visibly one-counter automata, we show that OCAs with counter observability are effectively determinizable and closed under all boolean operations. Moreover, it turns out that they are expressively equivalent to strong automata, in which transitions are guarded by MSO formulas over the natural numbers with successor
An Automata-Theoretic Approach to the Verification of Distributed Algorithms
We introduce an automata-theoretic method for the verification of distributed
algorithms running on ring networks. In a distributed algorithm, an arbitrary
number of processes cooperate to achieve a common goal (e.g., elect a leader).
Processes have unique identifiers (pids) from an infinite, totally ordered
domain. An algorithm proceeds in synchronous rounds, each round allowing a
process to perform a bounded sequence of actions such as send or receive a pid,
store it in some register, and compare register contents wrt. the associated
total order. An algorithm is supposed to be correct independently of the number
of processes. To specify correctness properties, we introduce a logic that can
reason about processes and pids. Referring to leader election, it may say that,
at the end of an execution, each process stores the maximum pid in some
dedicated register. Since the verification of distributed algorithms is
undecidable, we propose an underapproximation technique, which bounds the
number of rounds. This is an appealing approach, as the number of rounds needed
by a distributed algorithm to conclude is often exponentially smaller than the
number of processes. We provide an automata-theoretic solution, reducing model
checking to emptiness for alternating two-way automata on words. Overall, we
show that round-bounded verification of distributed algorithms over rings is
PSPACE-complete.Comment: 26 pages, 6 figure
One-Counter Automata with Counter Observability
International audienceIn a one-counter automaton (OCA), one can produce a letter from some finite alphabet, increment and decrement the counter by one, or compare it with constants up to some threshold. It is well-known that universality and language inclusion for OCAs are undecidable. In this paper, we consider OCAs with counter observability: Whenever the automaton produces a letter, it outputs the current counter value along with it. Hence, its language is now a set of words over an infinite alphabet. We show that universality and inclusion for that model are PSPACE-complete, thus no harder than the corresponding problems for finite automata. In fact, by establishing a link with visibly one-counter automata, we show that OCAs with counter observability are e ectively determinizable and closed under all boolean operations. Moreover, it turns out that they are expressively equivalent to strong automata, in which transitions are guarded by MSO formulas over the natural numbers with successor
Automata and Logics for Concurrent Systems: Realizability and Verification
Automata are a popular tool to make computer systems accessible to formal methods. While classical finite automata are suitable to model sequential boolean programs, models of concurrent systems involve several interacting processes and extend finite-state machines in various respects. This habilitation thesis surveys several such extensions, including pushdown automata with multiple stacks, communicating automata with fixed, parameterized, or dynamic communication topology, and automata running on words over infinite alphabets. We focus on two major questions of classical automata theory, namely realizability (asking whether a specification has an automata counterpart) and model checking (asking whether a given automaton satisfies its specification)
Parameterized Communicating Automata: Complementation and Model Checking
We study the language-theoretical aspects of parameterized communicating automata (PCAs), in which processes communicate via rendez-vous. A given PCA can be run on any topology of bounded degree such as pipelines, rings, ranked trees, and grids. We show that, under a context bound, which restricts the local behavior of each process, PCAs are effectively complementable. Complementability is considered a key aspect of robust automata models and can, in particular, be exploited for verification. In this paper, we use it to obtain a characterization of context-bounded PCAs in terms of monadic second-order (MSO) logic. As the emptiness problem for context-bounded PCAs is decidable for the classes of pipelines, rings, and trees, their model-checking problem wrt. MSO properties also becomes decidable. While previous work on model checking parameterized systems typically uses temporal logics without next operator, our MSO logic allows one to express several natural next modalities
Local First-Order Logic with Two Data Values
We study first-order logic over unordered structures whose elements carry two data values from an infinite domain. Data values can be compared wrt. equality so that the formalism is suitable to specify the input-output behavior of various distributed algorithms. As the logic is undecidable in general, we introduce a family of local fragments that restrict quantification to neighborhoods of a given reference point. Our main result establishes decidability of the satisfiability problem for one of these non-trivial local fragments. On the other hand, already slightly more general local logics turn out to be undecidable. Altogether, we draw a landscape of formalisms that are suitable for the specification of systems with data and open up new avenues for future research
Communicating Finite-State Machines and Two-Variable Logic
Communicating finite-state machines are a fundamental, well-studied model of finite-state processes that communicate via unbounded first-in first-out channels. We show that they are expressively equivalent to existential MSO logic with two first-order variables and the order relation
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