30 research outputs found
Advanced Automata Minimization
We present an efficient algorithm to reduce the size of nondeterministic
Buchi word automata, while retaining their language. Additionally, we describe
methods to solve PSPACE-complete automata problems like universality,
equivalence and inclusion for much larger instances (1-3 orders of magnitude)
than before. This can be used to scale up applications of automata in formal
verification tools and decision procedures for logical theories. The algorithm
is based on new transition pruning techniques. These use criteria based on
combinations of backward and forward trace inclusions. Since these relations
are themselves PSPACE-complete, we describe methods to compute good
approximations of them in polynomial time. Extensive experiments show that the
average-case complexity of our algorithm scales quadratically. The size
reduction of the automata depends very much on the class of instances, but our
algorithm consistently outperforms all previous techniques by a wide margin. We
tested our algorithm on Buchi automata derived from LTL-formulae, many classes
of random automata and automata derived from mutual exclusion protocols, and
compared its performance to the well-known automata tool GOAL.Comment: 15 page
Buffered Simulation Games for B\"uchi Automata
Simulation relations are an important tool in automata theory because they
provide efficiently computable approximations to language inclusion. In recent
years, extensions of ordinary simulations have been studied, for instance
multi-pebble and multi-letter simulations which yield better approximations and
are still polynomial-time computable.
In this paper we study the limitations of approximating language inclusion in
this way: we introduce a natural extension of multi-letter simulations called
buffered simulations. They are based on a simulation game in which the two
players share a FIFO buffer of unbounded size. We consider two variants of
these buffered games called continuous and look-ahead simulation which differ
in how elements can be removed from the FIFO buffer. We show that look-ahead
simulation, the simpler one, is already PSPACE-hard, i.e. computationally as
hard as language inclusion itself. Continuous simulation is even EXPTIME-hard.
We also provide matching upper bounds for solving these games with infinite
state spaces.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
Reducing Nondeterministic Tree Automata by Adding Transitions
We introduce saturation of nondeterministic tree automata, a technique that
consists of adding new transitions to an automaton while preserving its
language. We implemented our algorithm on minotaut - a module of the tree
automata library libvata that reduces the size of automata by merging states
and removing superfluous transitions - and we show how saturation can make
subsequent merge and transition-removal operations more effective. Thus we
obtain a Ptime algorithm that reduces the size of tree automata even more than
before. Additionally, we explore how minotaut alone can play an important role
when performing hard operations like complementation, allowing to both obtain
smaller complement automata and lower computation times. We then show how
saturation can extend this contribution even further. We tested our algorithms
on a large collection of automata from applications of libvata in shape
analysis, and on different classes of randomly generated automata.Comment: In Proceedings MEMICS 2016, arXiv:1612.0403
Incremental Dead State Detection in Logarithmic Time
Identifying live and dead states in an abstract transition system is a
recurring problem in formal verification; for example, it arises in our recent
work on efficiently deciding regex constraints in SMT. However,
state-of-the-art graph algorithms for maintaining reachability information
incrementally (that is, as states are visited and before the entire state space
is explored) assume that new edges can be added from any state at any time,
whereas in many applications, outgoing edges are added from each state as it is
explored. To formalize the latter situation, we propose guided incremental
digraphs (GIDs), incremental graphs which support labeling closed states
(states which will not receive further outgoing edges). Our main result is that
dead state detection in GIDs is solvable in amortized time per edge
for edges, improving upon per edge due to Bender, Fineman,
Gilbert, and Tarjan (BFGT) for general incremental directed graphs.
We introduce two algorithms for GIDs: one establishing the logarithmic time
bound, and a second algorithm to explore a lazy heuristics-based approach. To
enable an apples-to-apples experimental comparison, we implemented both
algorithms, two simpler baselines, and the state-of-the-art BFGT baseline using
a common directed graph interface in Rust. Our evaluation shows -x
speedups over BFGT for the largest input graphs over a range of graph classes,
random graphs, and graphs arising from regex benchmarks.Comment: 22 pages + reference