Motivated by the successful application of the theory of regular languages to formal verification of finite-state systems, there is a renewed interest in developing a theory of analyzable functions from strings to numerical values that can provide a foundation for analyzing quantitative properties of finitestate systems. In this paper, we propose a deterministic model for associating costs with strings that is parameterized by operations of interest (such as addition, scaling, and min), a notion of regularity that provides a yardstick to measure expressiveness, and study decision problems and theoretical properties of resulting classes of cost functions. Our definition of regularity relies on the theory of string-to-tree transducers, and allows associating costs with events that are conditional upon regular properties of future events. Our model of cost register automata allows computation of regular functions using multiple “write-only” registers whose values can be combined using the allowed set of operations. We show that classical shortest-path algorithms as well as algorithms designed for computing discounted costs, can be adopted for solving the min-cost problems for the more general classes of functions specified in our model. Cost register automata with min and increment give a deterministic model that is equivalent to weighted automata, an extensively studied nondeterministic model, and this connection results in new insights and new open problems.
Streaming tree transducers @cite_34 (STTs), introduced by two of the co-authors in this paper are a new formalism for expressing MSO-definable tree-to-tree and string-to-tree transductions. In comparison to some of the transducer models discussed above, STTs have distinguishing features that make them desirable as a canonical model for specifying regular or MSO-definable transductions: (1) STTs produce the output in linear time by performing a single pass over the input, (2) they preserve desirable properties such as closure under sequential composition and regular look-ahead, and (3) they have good algorithmic properties such as decidability of functional equivalence.
@cite_34
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Two well-known formalisms for the specification and computation of tree transductions are compared: the mso graph transducer and the attributed tree transducer with look-ahead, respectively. The mso graph transducer, restricted to trees, uses monadic second order logic to define the output tree in terms of the input tree. The attributed tree transducer is an attribute grammar in which all attributes are trees; it is preceded by a look-ahead phase in which all attributes have finitely many values. The main result is that these formalisms are equivalent, i.e., that the attributed tree transducer with look-ahead is an appropriate implementation model for the tree transductions that are specifiable in mso logic. This result holds for mso graph transducers that produce trees with shared subtrees. If no sharing is allowed, the attributed tree transducer satisfies the single use restriction. Theory of tree transducers provides a foundation for understanding expressiveness and complexity of analysis problems for specification languages for transforming hierarchically structured data such as XML documents. We introduce streaming tree transducers as an analyzable, executable, and expressive model for transforming unranked ordered trees in a single pass. Given a linear encoding of the input tree, the transducer makes a single left-to-right pass through the input, and computes the output in linear time using a finite-state control, a visibly pushdown stack, and a finite number of variables that store output chunks that can be combined using the operations of string-concatenation and tree-insertion. We prove that the expressiveness of the model coincides with transductions definable using monadic second-order logic (MSO). Existing models of tree transducers either cannot implement all MSO-definable transformations, or require regular look ahead that prohibits single-pass implementation. We show a variety of analysis problems such as type-checking and checking functional equivalence are solvable for our model. We extend a classic result of Buchi, Elgot, and Trakhtenbrot: MSO definable string transductions i.e., string-to-string functions that are definable by an interpretation using monadic second-order (MSO) logic, are exactly those realized by deterministic two-way finite-state transducers, i.e., finite-state automata with a two-way input tape and a one-way output tape. Consequently, the equivalence of two mso definable string transductions is decidable. In the nondeterministic case however, MSO definable string tranductions, i.e., binary relations on strings that are mso definable by an interpretation with parameters, are incomparable to those realized by nondeterministic two-way finite-state transducers. This is a motivation to look for another machine model, and we show that both classes of MSO definable string transductions are characterized in terms of Hennie machines, i.e., two-way finite-state transducers that are allowed to rewrite their input tape, but may visit each position of their input only a bounded number of times. A characterization is given of the class of tree translations definable in monadic second-order logic (MSO), in terms of macro tree transducers. The first main result is that the MSO definable tree translations are exactly those tree translations realized by macro tree transducers (MTTs) with regular look-ahead that are single use restricted. For this the single use restriction known from attribute grammars is generalized to MTTs. Since MTTs are closed under regular look-ahead, this implies that every MSO definable tree translation can be realized by an MTT. The second main result is that the class of MSO definable tree translations can also be obtained by restricting MTTs with regular look-ahead to be finite copying, i.e., to require that each input subtree is processed only a bounded number of times. The single use restriction is a rather strong, static restriction on the rules of an MTT, whereas the finite copying restriction is a more liberal, dynamic restriction on the derivations of an MTT. Macro tree transducers are a combination of top-down tree transducers and macro grammars. They serve as a model for syntax-directed semantics in which context information can be handled. In this paper the formal model of macro tree transducers is studied by investigating typical automata theoretical topics like composition, decomposition, domains, and ranges of the induced translation classes. The extension with regular look-ahead is considered. Location prediction has attracted a significant amount of research effort. Given an object's recent movements and a future time, the goal of location prediction is to predict the location of this object at the future time specified. Prior works have elaborated on mining association relationships among regions, in which objects frequently appear, to predict locations. Association relationships among regions are represented as association rules. By exploring association relationships among regions, prior works are able to have a good accuracy for location prediction. However, with a large amount of trajectory data produced, a huge amount of association rules is expected. Furthermore, trajectory data has both the spatial and temporal information. To further enhance the accuracy of location prediction, one could utilize not only spatial information but also temporal information to estimate locations of objects. In this paper, we propose a spatial-temporal trajectory model (abbreviated as STT) to capture movement behaviors of objects. STT is represented as a probabilistic suffix tree with both spatial and temporal information of movements. Note that STT is able to discover sequential traversal relationships among regions and, for each region, STT derives the corresponding probabilities about the time when objects appear. With the nature of probabilistic suffix tree, we could use a compact structure to capture movement behavior of objects compared to association rules proposed. In light of STT, we further propose an algorithm to traverse STT for location prediction. By exploring both the spatial and temporal information of STT, the accuracy of location prediction is improved. To evaluate our proposed STT and prediction algorithm, we conduct experiments on the synthetic dataset generated from real datasets. Experimental results shows that our proposed STT is able to capture both spatial and temporal patterns of movement behaviors and, by exploring STT, our proposed prediction algorithm outperforms existing works. We propose the model of nested words for representation of data with both a linear ordering and a hierarchically nested matching of items. Examples of data with such dual linear-hierarchical structure include executions of structured programs, annotated linguistic data, and HTML XML documents. Nested words generalize both words and ordered trees, and allow both word and tree operations. We define nested word automata—finite-state acceptors for nested words, and show that the resulting class of regular languages of nested words has all the appealing theoretical properties that the classical regular word languages enjoys: deterministic nested word automata are as expressive as their nondeterministic counterparts; the class is closed under union, intersection, complementation, concatenation, Kleene-*, prefixes, and language homomorphisms; membership, emptiness, language inclusion, and language equivalence are all decidable; and definability in monadic second order logic corresponds exactly to finite-state recognizability. We also consider regular languages of infinite nested words and show that the closure properties, MSO-characterization, and decidability of decision problems carry over. The linear encodings of nested words give the class of visibly pushdown languages of words, and this class lies between balanced languages and deterministic context-free languages. We argue that for algorithmic verification of structured programs, instead of viewing the program as a context-free language over words, one should view it as a regular language of nested words (or equivalently, a visibly pushdown language), and this would allow model checking of many properties (such as stack inspection, pre-post conditions) that are not expressible in existing specification logics. We also study the relationship between ordered trees and nested words, and the corresponding automata: while the analysis complexity of nested word automata is the same as that of classical tree automata, they combine both bottom-up and top-down traversals, and enjoy expressiveness and succinctness benefits over tree automata. We develop new algorithms for learning monadic node selection queries in unranked trees from annotated examples, and apply them to visually interactive Web information extraction. We propose to represent monadic queries by bottom-up deterministic Node Selecting Tree Transducers (NSTTs), a particular class of tree automata that we introduce. We prove that deterministic NSTTs capture the class of queries definable in monadic second order logic (MSO) in trees, which Gottlob and Koch (2002) argue to have the right expressiveness for Web information extraction, and prove that monadic queries defined by NSTTs can be answered efficiently. We present a new polynomial time algorithm in RPNI-style that learns monadic queries defined by deterministic NSTTs from completely annotated examples, where all selected nodes are distinguished. In practice, users prefer to provide partial annotations. We propose to account for partial annotations by intelligent tree pruning heuristics. We introduce pruning NSTTs--a formalism that shares many advantages of NSTTs. This leads us to an interactive learning algorithm for monadic queries defined by pruning NSTTs, which satisfies a new formal active learning model in the style of Angluin (1987). We have implemented our interactive learning algorithm integrated it into a visually interactive Web information extraction system--called SQUIRREL--by plugging it into the Mozilla Web browser. Experiments on realistic Web documents confirm excellent quality with very few user interactions during wrapper induction. We study languages of nested trees—structures obtained by augmenting trees with sets of nested jump-edges. These graphs can naturally model branching behaviors of pushdown programs, so that the problem of branching-time software model checking may be phrased as a membership question for such languages. We define finite-state automata accepting such languages—these automata can pass states along jump-edges as well as tree edges. We find that the model-checking problem for these automata on pushdown systems is EXPTIME-complete, and that their alternating versions are expressively equivalent to NT-μ, a recently proposed temporal logic for nested trees that can express a variety of branching-time, “context-free” requirements. We also show that monadic second order logic (MSO) cannot exploit the structure: MSO on nested trees is too strong in the sense that it has an undecidable model checking problem, and seems too weak to capture NT-μ. We propose a deterministic model for associating costs with strings that is parameterized by operations of interest (such as addition, scaling, and minimum), a notion of regularity that provides a yardstick to measure expressiveness, and study decision problems and theoretical properties of resulting classes of cost functions. Our definition of regularity relies on the theory of string-to-tree transducers, and allows associating costs with events that are conditioned on regular properties of future events. Our model of cost register automata allows computation of regular functions using multiple "write-only" registers whose values can be combined using the allowed set of operations. We show that the classical shortest-path algorithms as well as the algorithms designed for computing discounted costs can be adapted for solving the min-cost problems for the more general classes of functions specified in our model. Cost register automata with the operations of minimum and increment give a deterministic model that is equivalent to weighted automata, an extensively studied nondeterministic model, and this connection results in new insights and new open problems. A generalization from string to trees and from languages to translations is given of the classical result that any regular language can be learned from examples: it is shown that for any deterministic top-down tree transformation there exists a sample set of polynomial size (with respect to the minimal transducer) which allows to infer the translation. Until now, only for string transducers and for simple relabeling tree transducers, similar results had been known. Learning of deterministic top-down tree transducers (dtops) is far more involved because a dtop can copy, delete, and permute its input subtrees. Thus, complex dependencies of labeled input to output paths need to be maintained by the algorithm. First, a Myhill-Nerode theorem is presented for dtops, which is interesting on its own. This theorem is then used to construct a learning algorithm for dtops. Finally, it is shown how our result can be applied to xml transformations (e.g. xslt programs). For this, a new dtd-based encoding of unranked trees by ranked ones is presented. Over such encodings, dtops can realize many practically interesting xml transformations which cannot be realized on firstchild next-sibling encodings. Regular model checking is a form of symbolic model checking for parameterized and infinite-state systems whose states can be represented as words of arbitrary length over a finite alphabet, in which regular sets of words are used to represent sets of states. We present LTL(MSO), a combination of the logics monadic second-order logic (MSO) and LTL as a natural logic for expressing the temporal properties to be verified in regular model checking. In other words, LTL(MSO) is a natural specification language for both the system and the property under consideration. LTL(MSO) is a two-dimensional modal logic, where MSO is used for specifying properties of system states and transitions, and LTL is used for specifying temporal properties. In addition, the first-order quantification in MSO can be used to express properties parameterized on a position or process. We give a technique for model checking LTL(MSO), which is adapted from the automata-theoretic approach: a formula is translated to a buchi regular transition system with a regular set of accepting states, and regular model checking techniques are used to search for models. We have implemented the technique, and show its application to a number of parameterized algorithms from the literature. Spin-transfer torque random access memory (STT-RAM) has received increasing attention because of its attractive features: good scalability, zero standby power, non-volatility and radiation hardness. The use of STT-RAM technology in the last level on-chip caches has been proposed as it minimizes cache leakage power with technology scaling down. Furthermore, the cell area of STT-RAM is only 1 9 1 3 that of SRAM. This allows for a much larger cache with the same die footprint, improving overall system performance through reducing cache misses. However, deploying STT-RAM technology in L1 caches is challenging because of the long and power-consuming write operations. In this paper, we propose both L1 and lower level cache designs that use STT-RAM. In particular, our designs use STT-RAM cells with various data retention time and write performances, made possible by different magnetic tunneling junction (MTJ) designs. For the fast STT-RAM bits with reduced data retention time, a counter controlled dynamic refresh scheme is proposed to maintain the data validity. Our dynamic scheme saves more than 80 refresh energy compared to the simple refresh scheme proposed in previous works. A L1 cache built with ultra low retention STT-RAM coupled with our proposed dynamic refresh scheme can achieve 9.2 in performance improvement, and saves up to 30 of the total energy when compared to one that uses traditional SRAM. For lower level caches with relative large cache capacity, we propose a data migration scheme that moves data between portions of the cache with different retention characteristics so as to maximize the performance and power benefits. Our experiments show that on the average, our proposed multi retention level STT-RAM cache reduces 30 70 of the total energy compared to previous works, while improving IPC performance for both 2-level and 3-level cache hierarchy. Conventionally, regular expression matching (REM) has been performed by sequentially comparing the regular expression (regex) to the input stream, which can be slow due to excessive backtracking (smith:acsac06). Alternatively, the regex can be converted to a deterministic finite automaton (DFA) for efficient matching, which however may require an extremely large state transition table (STT) due to exponential state explosion (meyer:swat71, yu:ancs06). We propose the segmented regex-NFA (SR-NFA) architecture, where the regex is first compiled into modular nondeterministic finite automata (NFA), then partitioned, optimized, and matched efficiently on modern multi-core processors. SR-NFA offers attack-resilient multi-gigabit per second matching throughput, does not suffer from either backtracking or state explosion, and can be rapidly constructed. For regex sets that construct a DFA with moderate state explosion, i.e., on average 200k states in the STT, the proposed SR-NFA is 367k times faster to construct and update and use 23k times less memory than the DFA approach. Running on an 8-core 2.6 GHz Opteron platform, our prototype achieves 2.2 Gbps average matching throughput for regex sets with up to 4,000 SR-NFA states per regex set. Existential second-order logic (ESO) and monadic second-order logic(MSO) have attracted much interest in logic and computer science. ESO is a much expressive logic over successor structures than MSO. However, little was known about the relationship between MSOand syntatic fragments of ESO. We shed light on this issue by completely characterizing this relationship for the prefix classes of ESO over strings, (i.e., finite successor structures). Moreover, we determine the complexity of model checking over strings, for all ESO-prefix classes. Let ESO( Q ) denote the prefix class containing all sentences of the shape ∃R Q 4 , where R is a list of predicate variables, Q is a first-order predicate qualifier from the prefix set Q and 4 is quantifier-free. We show that ESO( ∃*∀∃* ) and ESO( ∃*∀∀ ) are the maximal standard ESO-prefix classes contained in MSO, thus expressing only regular languages. We further prove the following dichotomy theorem: An ESO prefix-class either expresses only regular languages (and is thus in MSO), or it expresses some NP-complete languages. We also give a precise characterization of those ESO-prefix classes that are equivalent to MSO over strings, and of the ESO-prefix classes which are closed under complementation on strings. Many semantic parsing models use tree transformations to map between natural language and meaning representation. However, while tree transformations are central to several state-of-the-art approaches, little use has been made of the rich literature on tree automata. This paper makes the connection concrete with a tree transducer based semantic parsing model and suggests that other models can be interpreted in a similar framework, increasing the generality of their contributions. In particular, this paper further introduces a variational Bayesian inference algorithm that is applicable to a wide class of tree transducers, producing state-of-the-art semantic parsing results while remaining applicable to any domain employing probabilistic tree transducers. Abstract.Due to their expressive power, regular expressions (REs) are quickly becoming an integral part of language specifications for several important application scenarios. Many of these applications have to manage huge databases of RE specifications and need to provide an effective matching mechanism that, given an input string, quickly identifies the REs in the database that match it. In this paper, we propose the RE-tree, a novel index structure for large databases of RE specifications. Given an input query string, the RE-tree speeds up the retrieval of matching REs by focusing the search and comparing the input string with only a small fraction of REs in the database. Even though the RE-tree is similar in spirit to other tree-based structures that have been proposed for indexing multidimensional data, RE indexing is significantly more challenging since REs typically represent infinite sets of strings with no well-defined notion of spatial locality. To address these new challenges, our RE-tree index structure relies on novel measures for comparing the relative sizes of infinite regular languages. We also propose innovative solutions for the various RE-tree operations including the effective splitting of RE-tree nodes and computing a "tight" bounding RE for a collection of REs. Finally, we demonstrate how sampling-based approximation algorithms can be used to significantly speed up the performance of RE-tree operations. Preliminary experimental results with moderately large synthetic data sets indicate that the RE-tree is effective in pruning the search space and easily outperforms naive sequential search approaches. Abstract A general problem in computational graph theory is that of finding an optimal subgraph H of a given weighted graph G . The matching problem (which is easy) and the traveling salesman problem (which is not) are well-known examples of this general problem. In the literature one can also find a variety of ad hoc algorithms for solving certain special cases in linear time. We suggest a general approach for constructing linear-time algorithms in the case where the graph G is defined by certain rules of composition (as are trees, series-parallel graphs, and outerplanar graphs) and the desired subgraph H satisfies a property that is “regular” with respect to these rules of composition (as do matchings, dominating sets, and independent sets for all the classes just mentioned). This approach is applied to obtain a linear-time algorithm for computing the irredundance number of a tree, a problem for which no polynomial-time algorithm was previously known. We propose semantic role features for a Tree-to-String transducer to model the reordering deletion of source-side semantic roles. These semantic features, as well as the Tree-to-String templates, are trained based on a conditional log-linear model and are shown to significantly outperform systems trained based on Max-Likelihood and EM. We also show significant improvement in sentence fluency by using the semantic role features in the log-linear model, based on manual evaluation. Computations on trees form a classical topic in computing. These computations can be described in terms of machines (typically called tree transducers), or in terms of functions. This paper focuses on three flavors of bottom-up computations, of increasing generality. It brings categorical clarity by identifying a category of tree transducers together with two different behavior functors. The first sends a tree transducer to a coKleisli or biKleisli map (describing the contribution of each local node in an input tree to the global transformation) and the second to a tree function (the global tree transformation). The first behavior functor has an adjoint realization functor, like in Goguen's early work on automata. Further categorical structure, in the form of Hughes's Arrows, appears in properly parameterized versions of these structures.