6,412 research outputs found
Synthesis of Data Word Transducers
In reactive synthesis, the goal is to automatically generate an
implementation from a specification of the reactive and non-terminating
input/output behaviours of a system. Specifications are usually modelled as
logical formulae or automata over infinite sequences of signals
(-words), while implementations are represented as transducers. In the
classical setting, the set of signals is assumed to be finite. In this paper,
we consider data -words instead, i.e., words over an infinite alphabet.
In this context, we study specifications and implementations respectively given
as automata and transducers extended with a finite set of registers. We
consider different instances, depending on whether the specification is
nondeterministic, universal or deterministic, and depending on whether the
number of registers of the implementation is given or not.
In the unbounded setting, we show undecidability for both universal and
nondeterministic specifications, while decidability is recovered in the
deterministic case. In the bounded setting, undecidability still holds for
nondeterministic specifications, but can be recovered by disallowing tests over
input data. The generic technique we use to show the latter result allows us to
reprove some known result, namely decidability of bounded synthesis for
universal specifications
A Linear-Time Nominal ?-Calculus with Name Allocation
Logics and automata models for languages over infinite alphabets, such as Freeze LTL and register automata, serve the verification of processes or documents with data. They relate tightly to formalisms over nominal sets, such as nondetermininistic orbit-finite automata (NOFAs), where names play the role of data. Reasoning problems in such formalisms tend to be computationally hard. Name-binding nominal automata models such as {regular nondeterministic nominal automata (RNNAs)} have been shown to be computationally more tractable. In the present paper, we introduce a linear-time fixpoint logic Bar-?TL} for finite words over an infinite alphabet, which features full negation and freeze quantification via name binding. We show by a nontrivial reduction to extended regular nondeterministic nominal automata that even though Bar-?TL} allows unrestricted nondeterminism and unboundedly many registers, model checking Bar-?TL} over RNNAs and satisfiability checking both have elementary complexity. For example, model checking is in 2ExpSpace, more precisely in parametrized ExpSpace, effectively with the number of registers as the parameter
Relating timed and register automata
Timed automata and register automata are well-known models of computation
over timed and data words respectively. The former has clocks that allow to
test the lapse of time between two events, whilst the latter includes registers
that can store data values for later comparison. Although these two models
behave in appearance differently, several decision problems have the same
(un)decidability and complexity results for both models. As a prominent
example, emptiness is decidable for alternating automata with one clock or
register, both with non-primitive recursive complexity. This is not by chance.
This work confirms that there is indeed a tight relationship between the two
models. We show that a run of a timed automaton can be simulated by a register
automaton, and conversely that a run of a register automaton can be simulated
by a timed automaton. Our results allow to transfer complexity and decidability
results back and forth between these two kinds of models. We justify the
usefulness of these reductions by obtaining new results on register automata.Comment: In Proceedings EXPRESS'10, arXiv:1011.601
On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection
Extended regular expressions (with complement and intersection) are used in many applications due to their succinctness. In particular, regular expressions extended with intersection only (also called semi-extended) can already be exponentially smaller than standard regular expressions or equivalent nondeterministic finite automata (NFA). For practical purposes it is important to study the average behaviour of conversions between these models. In this paper, we focus on the conversion of regular expressions with intersection to nondeterministic finite automata, using partial derivatives and the notion of support. First, we give a tight upper bound of 2O(n) for the worst-case number of states of the resulting partial derivative automaton, where n is the size of the expression. Using the framework of analytic combinatorics, we then establish an upper bound of (1.056 + o(1))n for its asymptotic average-state complexity, which is significantly smaller than the one for the worst case. (c) IFIP International Federation for Information Processing 2016
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