879 research outputs found
Hyper-Minimization for Deterministic Weighted Tree Automata
Hyper-minimization is a state reduction technique that allows a finite change
in the semantics. The theory for hyper-minimization of deterministic weighted
tree automata is provided. The presence of weights slightly complicates the
situation in comparison to the unweighted case. In addition, the first
hyper-minimization algorithm for deterministic weighted tree automata, weighted
over commutative semifields, is provided together with some implementation
remarks that enable an efficient implementation. In fact, the same run-time O(m
log n) as in the unweighted case is obtained, where m is the size of the
deterministic weighted tree automaton and n is its number of states.Comment: In Proceedings AFL 2014, arXiv:1405.527
State Space Reduction For Parity Automata
Exact minimization of ?-automata is a difficult problem and heuristic algorithms are a subject of current research. We propose several new approaches to reduce the state space of deterministic parity automata. These are based on extracting information from structures within the automaton, such as strongly connected components, coloring of the states, and equivalence classes of given relations, to determine states that can safely be merged. We also establish a framework to generalize the notion of quotient automata and uniformly describe such algorithms. The description of these procedures consists of a theoretical analysis as well as data collected from experiments
More Structural Characterizations of Some Subregular Language Families by Biautomata
We study structural restrictions on biautomata such as, e.g., acyclicity,
permutation-freeness, strongly permutation-freeness, and orderability, to
mention a few. We compare the obtained language families with those induced by
deterministic finite automata with the same property. In some cases, it is
shown that there is no difference in characterization between deterministic
finite automata and biautomata as for the permutation-freeness, but there are
also other cases, where it makes a big difference whether one considers
deterministic finite automata or biautomata. This is, for instance, the case
when comparing strongly permutation-freeness, which results in the family of
definite language for deterministic finite automata, while biautomata induce
the family of finite and co-finite languages. The obtained results nicely fall
into the known landscape on classical language families.Comment: In Proceedings AFL 2014, arXiv:1405.527
Minimization and Canonization of GFG Transition-Based Automata
While many applications of automata in formal methods can use
nondeterministic automata, some applications, most notably synthesis, need
deterministic or good-for-games(GFG) automata. The latter are nondeterministic
automata that can resolve their nondeterministic choices in a way that only
depends on the past. The minimization problem for deterministic B\"uchi and
co-B\"uchi word automata is NP-complete. In particular, no canonical minimal
deterministic automaton exists, and a language may have different minimal
deterministic automata. We describe a polynomial minimization algorithm for GFG
co-B\"uchi word automata with transition-based acceptance. Thus, a run is
accepting if it traverses a set of designated transitions only
finitely often. Our algorithm is based on a sequence of transformations we
apply to the automaton, on top of which a minimal quotient automaton is
defined. We use our minimization algorithm to show canonicity for
transition-based GFG co-B\"uchi word automata: all minimal automata have
isomorphic safe components (namely components obtained by restricting the
transitions to these not in ) and once we saturate the automata with
-transitions, we get full isomorphism.Comment: 28 pages, 9 figures. arXiv admin note: substantial text overlap with
arXiv:2009.1088
The Almost Equivalence by Asymptotic Probabilities for Regular Languages and Its Computational Complexities
We introduce p-equivalence by asymptotic probabilities, which is a weak
almost-equivalence based on zero-one laws in finite model theory. In this
paper, we consider the computational complexities of p-equivalence problems for
regular languages and provide the following details. First, we give an
robustness of p-equivalence and a logical characterization for p-equivalence.
The characterization is useful to generate some algorithms for p-equivalence
problems by coupling with standard results from descriptive complexity. Second,
we give the computational complexities for the p-equivalence problems by the
logical characterization. The computational complexities are the same as for
the (fully) equivalence problems. Finally, we apply the proofs for
p-equivalence to some generalized equivalences.Comment: In Proceedings GandALF 2016, arXiv:1609.0364
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