4 research outputs found
Feasible Automata for Two-Variable Logic with Successor on Data Words
We introduce an automata model for data words, that is words that carry at
each position a symbol from a finite alphabet and a value from an unbounded
data domain. The model is (semantically) a restriction of data automata,
introduced by Bojanczyk, et. al. in 2006, therefore it is called weak data
automata. It is strictly less expressive than data automata and the expressive
power is incomparable with register automata. The expressive power of weak data
automata corresponds exactly to existential monadic second order logic with
successor +1 and data value equality \sim, EMSO2(+1,\sim). It follows from
previous work, David, et. al. in 2010, that the nonemptiness problem for weak
data automata can be decided in 2-NEXPTIME. Furthermore, we study weak B\"uchi
automata on data omega-strings. They can be characterized by the extension of
EMSO2(+1,\sim) with existential quantifiers for infinite sets. Finally, the
same complexity bound for its nonemptiness problem is established by a
nondeterministic polynomial time reduction to the nonemptiness problem of weak
data automata.Comment: 21 page
Reasoning about Data Repetitions with Counter Systems
We study linear-time temporal logics interpreted over data words with
multiple attributes. We restrict the atomic formulas to equalities of attribute
values in successive positions and to repetitions of attribute values in the
future or past. We demonstrate correspondences between satisfiability problems
for logics and reachability-like decision problems for counter systems. We show
that allowing/disallowing atomic formulas expressing repetitions of values in
the past corresponds to the reachability/coverability problem in Petri nets.
This gives us 2EXPSPACE upper bounds for several satisfiability problems. We
prove matching lower bounds by reduction from a reachability problem for a
newly introduced class of counter systems. This new class is a succinct version
of vector addition systems with states in which counters are accessed via
pointers, a potentially useful feature in other contexts. We strengthen further
the correspondences between data logics and counter systems by characterizing
the complexity of fragments, extensions and variants of the logic. For
instance, we precisely characterize the relationship between the number of
attributes allowed in the logic and the number of counters needed in the
counter system.Comment: 54 page
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)