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首页> 外文会议>Annual ACM/IEEE Symposium on Logic in Computer Science >A Generalised Twinning Property for Minimisation of Cost Register Automata*
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A Generalised Twinning Property for Minimisation of Cost Register Automata*

机译：用于最小化成本寄存器自动机的推广孪晶性能*

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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,?) 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?c, with c ? M. This class is denoted by CRA?cM. 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,?) 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 CRA?c(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,?) : 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 ?, for some natural ?. Moreover, we show that if the operation ? 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 CRA?c(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.
机译：加权自动机（WA）通过用来自一个半环小号过渡权重相关联，定义函数从字S.最近延伸有限状态自动机，成本寄存器自动机（CRA）已被引入作为替代模型来描述由WA实现任何功能通过确定性机器的装置。在半群（M ,?）不含糊WA可以等效地由成本寄存器自动机，它的寄存器采取它们在M个值进行说明，通过以下形式的X操作更新：？= Y C，采用c？ M.该类由CRA表示<子的xmlns：MML = “http://www.w3.org/1998/Math/MathML” 的xmlns：的xlink = “http://www.w3.org/1999/xlink”> 2 C M.我们引入一个孪晶性质以及由整数k，使得对应的概念为，其中k = 1，获得有限状态转换器最初引入由Choffrut parametrised有界变化属性。鉴于以上的infinitary组（G ,?）实现一些函数f的明确加权自动机W，我们证明了以下三个性能是等效的：ⅰ）w满足k阶孪晶属性，ⅱ）f满足第k界变差属性，以及iii）f可以被通过CRA描述<子的xmlns：MML = “http://www.w3.org/1998/Math/MathML” 的xmlns：的xlink = “http://www.w3.org/1999/xlink”> 2 C （G）与至多为k registers.In tranducers的精神，我们实际上在更一般的设置通过考虑机器超过有限集从（G ,?）元件的半环证明这一结果：三种性能仍等效这样有限量值的加权自动机，即只是那些基数的的G字子集相关联至多？，对于一些天然？。此外，我们表明，如果操作？的G是可交换并且可计算，那么可以决定是否满足WA k阶的孪晶属性。作为一个必然结果，这使得决定为类CRA寄存器最小化问题<子的xmlns：MML = “http://www.w3.org/1998/Math/MathML” 的xmlns：的xlink = “http://www.w3.org/1999/xlink”> 2 C （G）。最后，我们证明了类似的结果适用于有限值有限状态传感器，并且，对于类CRA寄存器最小化问题。 c （B. * ）是PSPACE完成。

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