3,855 research outputs found
*-Continuous Kleene -Algebras for Energy Problems
Energy problems are important in the formal analysis of embedded or
autonomous systems. Using recent results on star-continuous Kleene
omega-algebras, we show here that energy problems can be solved by algebraic
manipulations on the transition matrix of energy automata. To this end, we
prove general results about certain classes of finitely additive functions on
complete lattices which should be of a more general interest.Comment: In Proceedings FICS 2015, arXiv:1509.0282
Synchronizing weighted automata
We introduce two generalizations of synchronizability to automata with
transitions weighted in an arbitrary semiring K=(K,+,*,0,1). (or equivalently,
to finite sets of matrices in K^nxn.) Let us call a matrix A
location-synchronizing if there exists a column in A consisting of nonzero
entries such that all the other columns of A are filled by zeros. If
additionally all the entries of this designated column are the same, we call A
synchronizing. Note that these notions coincide for stochastic matrices and
also in the Boolean semiring. A set M of matrices in K^nxn is called
(location-)synchronizing if M generates a matrix subsemigroup containing a
(location-)synchronizing matrix. The K-(location-)synchronizability problem is
the following: given a finite set M of nxn matrices with entries in K, is it
(location-)synchronizing?
Both problems are PSPACE-hard for any nontrivial semiring. We give sufficient
conditions for the semiring K when the problems are PSPACE-complete and show
several undecidability results as well, e.g. synchronizability is undecidable
if 1 has infinite order in (K,+,0) or when the free semigroup on two generators
can be embedded into (K,*,1).Comment: In Proceedings AFL 2014, arXiv:1405.527
A Generalised Twinning Property for Minimisation of Cost Register Automata
Weighted automata (WA) extend finite-state automata by associating with transitions weights from a semiring S, defining functions from words to S. Recently, cost register automata (CRA) have been introduced as an alternative model to describe any function realised by a WA by means of a deterministic machine. Unambiguous WA over a monoid (M, â) can equivalently be described by cost register automata whose registers take their values in M, and are updated by operations of the form x: = y â c, with c â M. This class is denoted by CRAâc(M).
We introduce a twinning property and a bounded variation property parametrised by an integer k, such that the corresponding notions introduced originally by Choffrut for finite-state transducers are obtained for k = 1. Given an unambiguous weighted automaton W over an infinitary group (G, â) realizing some function f, we prove that the three following properties are equivalent: i) W satisfies the twinning property of order k, ii) f satisfies the k-bounded variation property, and iii) f can be described by a CRAâc(G) with at most k registers.
In the spirit of tranducers, we actually prove this result in a more general setting by considering machines over the semiring of finite sets of elements from (G, â): the three properties are still equivalent for such finite-valued weighted automata, that is the ones associating with words subsets of G of cardinality at most â, for some natural â. Moreover, we show that if the operation â of G is commutative and computable, then one can decide whether a WA satisfies the twinning property of order k. As a corollary, this allows to decide the register minimisation problem for the class CRAâc(G).
Last, we prove that a similar result holds for finite-valued finite-state transducers, and that the register minimisation problem for the class CRA.c (B*) is Pspace-complete
Degree of Sequentiality of Weighted Automata
Weighted automata (WA) are an important formalism to describe quantitative properties. Obtaining equivalent deterministic machines is a longstanding research problem. In this paper we consider WA with a set semantics, meaning that the semantics is given by the set of weights of accepting runs. We focus on multi-sequential WA that are defined as finite unions of sequential WA. The problem we address is to minimize the size of this union. We call this minimum the degree of sequentiality of (the relation realized by) the WA.
For a given positive integer k, we provide multiple characterizations of relations realized by a union of k sequential WA over an infinitary finitely generated group: a Lipschitz-like machine independent property, a pattern on the automaton (a new twinning property) and a subclass of cost register automata. When possible, we effectively translate a WA into an equivalent union of k sequential WA. We also provide a decision procedure for our twinning property for commutative computable groups thus allowing to compute the degree of sequentiality. Last, we show that these results also hold for word transducers and that the associated decision problem is PSPACE
-complete
Towards a Uniform Theory of Effectful State Machines
Using recent developments in coalgebraic and monad-based semantics, we
present a uniform study of various notions of machines, e.g. finite state
machines, multi-stack machines, Turing machines, valence automata, and weighted
automata. They are instances of Jacobs' notion of a T-automaton, where T is a
monad. We show that the generic language semantics for T-automata correctly
instantiates the usual language semantics for a number of known classes of
machines/languages, including regular, context-free, recursively-enumerable and
various subclasses of context free languages (e.g. deterministic and real-time
ones). Moreover, our approach provides new generic techniques for studying the
expressivity power of various machine-based models.Comment: final version accepted by TOC
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