34 research outputs found
The equality problem for rational series with multiplicities in the tropical semiring is undecidable
We show that the equality problem for rational series with multiplicities in the tropical semiring is undecidable
The equality problem for rational series with multiplicities in the tropical semiring is undecidable
We show that the equality problem for rational series with multiplicities in the tropical semiring is undecidable
Series which are both max-plus and min-plus rational are unambiguous
Consider partial maps from the free monoid into the field of real numbers
with a rational domain. We show that two families of such series are actually
the same: the unambiguous rational series on the one hand, and the max-plus and
min-plus rational series on the other hand. The decidability of equality was
known to hold in both families with different proofs, so the above unifies the
picture. We give an effective procedure to build an unambiguous automaton from
a max-plus automaton and a min-plus one that recognize the same series
On Determinism and Unambiguity of Weighted Two-way Automata
In this paper, we first study the conversion of weighted two-way automata to
one-way automata. We show that this conversion preserves the unambiguity but
does not preserve the determinism. Yet, we prove that the conversion of an
unambiguous weighted one-way automaton into a two-way automaton leads to a
deterministic two-way automaton. As a consequence, we prove that unambiguous
weighted two-way automata are equivalent to deterministic weighted two-way
automata in commutative semirings.Comment: In Proceedings AFL 2014, arXiv:1405.527
On the Complexity of the Equivalence Problem for Probabilistic Automata
Checking two probabilistic automata for equivalence has been shown to be a
key problem for efficiently establishing various behavioural and anonymity
properties of probabilistic systems. In recent experiments a randomised
equivalence test based on polynomial identity testing outperformed
deterministic algorithms. In this paper we show that polynomial identity
testing yields efficient algorithms for various generalisations of the
equivalence problem. First, we provide a randomized NC procedure that also
outputs a counterexample trace in case of inequivalence. Second, we show how to
check for equivalence two probabilistic automata with (cumulative) rewards. Our
algorithm runs in deterministic polynomial time, if the number of reward
counters is fixed. Finally we show that the equivalence problem for
probabilistic visibly pushdown automata is logspace equivalent to the
Arithmetic Circuit Identity Testing problem, which is to decide whether a
polynomial represented by an arithmetic circuit is identically zero.Comment: technical report for a FoSSaCS'12 pape
Algebraic Elimination of epsilon-transitions
We present here algebraic formulas associating a k-automaton to a
k-epsilon-automaton. The existence depends on the definition of the star of
matrices and of elements in the semiring k. For this reason, we present the
theorem which allows the transformation of k-epsilon-automata into k-automata.
The two automata have the same behaviour.Comment: 13 decembre 200
Isomorphisms of scattered automatic linear orders
We prove that the isomorphism of scattered tree automatic linear orders as
well as the existence of automorphisms of scattered word automatic linear
orders are undecidable. For the existence of automatic automorphisms of word
automatic linear orders, we determine the exact level of undecidability in the
arithmetical hierarchy