31 research outputs found
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Reset Sequences for Finite Automata with Application to Design of Parts Orienters
Natarajan reduced the problem of designing a certain type of mechanical parts orienter to that of finding reset sequences for monotonic deterministic finite automata. He gave algorithms that in polynomial time either find such sequences or prove that no such sequence exists. In this paper we present a new algorithm based on breadth first search that runs in faster asymptotic time than Natarajan's algorithms, and in addition finds the shortest possible reset sequence if such a sequence exists. We give tight bounds on the length of the minimum reset sequence. We further improve the time and space bounds of another algorithm given by Natarajan, which finds reset sequences for general automata in the special case that all states are initially possible
Using Sat solvers for synchronization issues in partial deterministic automata
We approach the task of computing a carefully synchronizing word of minimum
length for a given partial deterministic automaton, encoding the problem as an
instance of SAT and invoking a SAT solver. Our experimental results demonstrate
that this approach gives satisfactory results for automata with up to 100
states even if very modest computational resources are used.Comment: 15 pages, 3 figure
Boosting expensive synchronizing heuristics
For automata, synchronization, the problem of bringing an automaton to a particular state regardless of its initial state, is important. It has several applications in practice and is related to a fifty-year-old conjecture on the length of the shortest synchronizing word. Although using shorter words increases the effectiveness in practice, finding a shortest one (which is not necessarily unique) is NP-hard. For this reason, there exist various heuristics in the literature. However, high-quality heuristics such as SynchroP producing relatively shorter sequences are very expensive and can take hours when the automaton has tens of thousands of states. The SynchroP heuristic has been frequently used as a benchmark to evaluate the performance of the new heuristics. In this work, we first improve the runtime of SynchroP and its variants by using algorithmic techniques. We then focus on adapting SynchroP for many-core architectures,
and overall, we obtain more than 1000× speedup on GPUs compared to naive sequential implementation that has been frequently used as a benchmark to evaluate new heuristics in the literature. We also propose two SynchroP variants and evaluate their performance
Checking Whether an Automaton Is Monotonic Is NP-complete
An automaton is monotonic if its states can be arranged in a linear order
that is preserved by the action of every letter. We prove that the problem of
deciding whether a given automaton is monotonic is NP-complete. The same result
is obtained for oriented automata, whose states can be arranged in a cyclic
order. Moreover, both problems remain hard under the restriction to binary
input alphabets.Comment: 13 pages, 4 figures. CIAA 2015. The final publication is available at
http://link.springer.com/chapter/10.1007/978-3-319-22360-5_2
Experiments on synchronizing automata
This work is motivated by the Černý Conjecture – an old unsolved problem in the automata theory. We describe the results of the experiments on synchronizing automata, which have led us to two interesting results. The first one is that the size of an automaton alphabet may play an important role in the issue of synchronization: we have found a 5-state automaton over a 3-letter alphabet which attains the upper bound from the Černý Conjecture, while there is no such automaton (except Černý automaton ) over a binary alphabet. The second result emerging from the experiments is a theorem describing the dependencies between the automaton structure expressed in terms of the so-called merging system and the maximal length of all minimal synchronizing words for automata of type