6,508 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
Minimization via duality
We show how to use duality theory to construct minimized versions of a wide class of automata. We work out three cases in detail: (a variant of) ordinary automata, weighted automata and probabilistic automata. The basic idea is that instead of constructing a maximal quotient we go to the dual and look for a minimal subalgebra and then return to the original category. Duality ensures that the minimal subobject becomes the maximally quotiented object
Automata in SageMath---Combinatorics meet Theoretical Computer Science
The new finite state machine package in the mathematics software system
SageMath is presented and illustrated by many examples. Several combinatorial
problems, in particular digit problems, are introduced, modeled by automata and
transducers and solved using SageMath. In particular, we compute the asymptotic
Hamming weight of a non-adjacent-form-like digit expansion, which was not known
before
Adaptive Intelligent Tutoring System for learning Computer Theory
In this paper, we present an intelligent tutoring system developed to help students in learning Computer Theory. The Intelligent tutoring system was built using ITSB authoring tool. The system helps students to learn finite automata, pushdown automata, Turing machines and examines the relationship between these automata and formal languages, deterministic and nondeterministic machines, regular expressions, context free grammars, undecidability, and complexity. During the process the intelligent tutoring system gives assistance and feedback of many types in an intelligent manner according to the behavior of the student. An evaluation of the intelligent tutoring system has revealed reasonably acceptable results in terms of its usability and learning abilities are concerned
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
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