216 research outputs found
Register automata with linear arithmetic
We propose a novel automata model over the alphabet of rational numbers,
which we call register automata over the rationals (RA-Q). It reads a sequence
of rational numbers and outputs another rational number. RA-Q is an extension
of the well-known register automata (RA) over infinite alphabets, which are
finite automata equipped with a finite number of registers/variables for
storing values. Like in the standard RA, the RA-Q model allows both equality
and ordering tests between values. It, moreover, allows to perform linear
arithmetic between certain variables. The model is quite expressive: in
addition to the standard RA, it also generalizes other well-known models such
as affine programs and arithmetic circuits.
The main feature of RA-Q is that despite the use of linear arithmetic, the
so-called invariant problem---a generalization of the standard non-emptiness
problem---is decidable. We also investigate other natural decision problems,
namely, commutativity, equivalence, and reachability. For deterministic RA-Q,
commutativity and equivalence are polynomial-time inter-reducible with the
invariant problem
Logics with rigidly guarded data tests
The notion of orbit finite data monoid was recently introduced by Bojanczyk
as an algebraic object for defining recognizable languages of data words.
Following Buchi's approach, we introduce a variant of monadic second-order
logic with data equality tests that captures precisely the data languages
recognizable by orbit finite data monoids. We also establish, following this
time the approach of Schutzenberger, McNaughton and Papert, that the
first-order fragment of this logic defines exactly the data languages
recognizable by aperiodic orbit finite data monoids. Finally, we consider
another variant of the logic that can be interpreted over generic structures
with data. The data languages defined in this variant are also recognized by
unambiguous finite memory automata
A Robust Class of Data Languages and an Application to Learning
We introduce session automata, an automata model to process data words, i.e.,
words over an infinite alphabet. Session automata support the notion of fresh
data values, which are well suited for modeling protocols in which sessions
using fresh values are of major interest, like in security protocols or ad-hoc
networks. Session automata have an expressiveness partly extending, partly
reducing that of classical register automata. We show that, unlike register
automata and their various extensions, session automata are robust: They (i)
are closed under intersection, union, and (resource-sensitive) complementation,
(ii) admit a symbolic regular representation, (iii) have a decidable inclusion
problem (unlike register automata), and (iv) enjoy logical characterizations.
Using these results, we establish a learning algorithm to infer session
automata through membership and equivalence queries
Supported Sets - A New Foundation for Nominal Sets and Automata
The present work proposes and discusses the category of supported sets which provides a uniform foundation for nominal sets of various kinds, such as those for equality symmetry, for the order symmetry, and renaming sets. We show that all these differently flavoured categories of nominal sets are monadic over supported sets. Thus, supported sets provide a canonical finite way to represent nominal sets and the automata therein, e.g. register automata and coalgebras in general. Name binding in supported sets is modelled by a functor following the idea of de Bruijn indices. This functor lifts to the well-known abstraction functor in nominal sets. Together with the monadicity result, this gives rise to a transformation process from finite coalgebras in supported sets to orbit-finite coalgebras in nominal sets. One instance of this process transforms the finite representation of a register automaton in supported sets into its configuration automaton in nominal sets
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