The Complexity of Downward Closure Comparisons

The downward closure of a language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of every language is regular. Moreover, recent results show that downward closures are computable for quite powerful system models. One advantage of abstracting a language by its downward closure is that then equivalence and inclusion become decidable. In this work, we study the complexity of these two problems. More precisely, we consider the following decision problems: Given languages K and L from classes C and D, respectively, does the downward closure of K include (equal) that of L? These problems are investigated for finite automata, one-counter automata, context-free grammars, and reversal-bounded counter automata. For each combination, we prove a completeness result either for fixed or for arbitrary alphabets. Moreover, for Petri net languages, we show that both problems are Ackermann-hard and for higher-order pushdown automata of order k, we prove hardness for complements of nondeterministic k-fold exponential time

Measuring autonomy and emergence via Granger causality

Concepts of emergence and autonomy are central to artificial life and related cognitive and behavioral sciences. However, quantitative and easy-to-apply measures of these phenomena are mostly lacking. Here, I describe quantitative and practicable measures for both autonomy and emergence, based on the framework of multivariate autoregression and specifically Granger causality. G-autonomy measures the extent to which the knowing the past of a variable helps predict its future, as compared to predictions based on past states of external (environmental) variables. G-emergence measures the extent to which a process is both dependent upon and autonomous from its underlying causal factors. These measures are validated by application to agent-based models of predation (for autonomy) and flocking (for emergence). In the former, evolutionary adaptation enhances autonomy; the latter model illustrates not only emergence but also downward causation. I end with a discussion of relations among autonomy, emergence, and consciousness

Implementing Groundness Analysis with Definite Boolean Functions

The domain of definite Boolean functions, Def, can be used to express the groundness of, and trace grounding dependencies between, program variables in (constraint) logic programs. In this paper, previously unexploited computational properties of Def are utilised to develop an efficient and succinct groundness analyser that can be coded in Prolog. In particular, entailment checking is used to prevent unnecessary least upper bound calculations. It is also demonstrated that join can be defined in terms of other operations, thereby eliminating code and removing the need for preprocessing formulae to a normal form. This saves space and time. Furthermore, the join can be adapted to straightforwardly implement the downward closure operator that arises in set sharing analyses. Experimental results indicate that the new Def implementation gives favourable results in comparison with BDD-based groundness analyses

Efficient Groundness Analysis in Prolog

Boolean functions can be used to express the groundness of, and trace grounding dependencies between, program variables in (constraint) logic programs. In this paper, a variety of issues pertaining to the efficient Prolog implementation of groundness analysis are investigated, focusing on the domain of definite Boolean functions, Def. The systematic design of the representation of an abstract domain is discussed in relation to its impact on the algorithmic complexity of the domain operations; the most frequently called operations should be the most lightweight. This methodology is applied to Def, resulting in a new representation, together with new algorithms for its domain operations utilising previously unexploited properties of Def -- for instance, quadratic-time entailment checking. The iteration strategy driving the analysis is also discussed and a simple, but very effective, optimisation of induced magic is described. The analysis can be implemented straightforwardly in Prolog and the use of a non-ground representation results in an efficient, scalable tool which does not require widening to be invoked, even on the largest benchmarks. An extensive experimental evaluation is givenComment: 31 pages To appear in Theory and Practice of Logic Programmin

Urban School Decentralization and the Growth of "Portfolio Districts"

In the latter half of the past decade, school districts in several large cities, including New York, Chicago, Washington, D.C., and post-Katrina New Orleans, have implemented an urban school decentralization model generally known as "portfolio districts." Others, including those in Denver and Cleveland, are following suit in what appears to be a growing trend. The portfolio strategy has become increasingly prominent in educational policy circles, think tank and philanthropy literature, and education news reporting. As CEO of the Chicago Public Schools, Arne Duncan embraced the portfolio district model. His appointment as U.S. Secretary of Education suggests the Obama administration also supports the approach. The premise of the portfolio strategy is that if superintendents build portfolios of schools that encompass a variety of educational approaches offered by different vendors, then over time school districts will weed out under-performing approaches and vendors; as a result, more children will have more opportunities for academic success. This brief examines the available evidence for the viability of this premise and the proposals that flow from it.The portfolio district approach merges four strategies: 1) decentralization; 2) charter school expansion; 3) reconstituting/closing "failing" schools; and 4) test-based accountability. Additionally, portfolio district restructuring often involves firing an underperforming school's staff in its entirety, whether or not the school is reconstituted as a charter school. In this model, the portfolio district is conceptualized as a circuit of "continuous improvement." Schools are assessed based on test scores; if their scores are low, they are subject to being closed and reopened as charters. The replacement charters are subsequently subject to test-based assessment and, if scores remain disappointing, to possible closure and replacement by still other contractors. The portfolio district concept implements what has been since the 1990's discussed in educational policy literature as market-based "creative destruction" or "churn."1 This perspective considers public schools to be comparable to private enterprise, with competition a key element to success. Just as businesses that cannot turn sufficient profit, schools that cannot produce test scores higher than competitors' must be "allowed" to "go out of business." The appeal of the portfolio district strategy is that it appears to offer an approach sufficiently radical to address longstanding and intractable problems in public schools.Although the strategy is being advocated by some policy centers, implemented by some large urban districts, and promoted by the education reforms proposed as part of the Obama administrations Race to the Top initiative, no peer-reviewed studies of portfolio districts exist, meaning that no reliable empirical evidence about portfolio effects is available that supports either the implementation or rejection of the portfolio district reform model. Nor is such evidence likely to be forthcoming. Even advocates acknowledge the enormous difficulty of designing credible empirical studies to determine how the portfolio approach affects student achievement and other outcomes. There are anecdotal reports of achievement gains in one portfolio district, New Orleans. The New Orleans results, however, have been subjected to serious challenge. Extrapolation of research on the constituent elements of the model is not helpful because of the complex interactions of these elements within the portfolio model. Moreover, even when the constituent elements are considered as a way to predict the likely success of the model, no evidence is found to suggest that it will produce gains in either achievement or fiscal efficiency. Finally, the policy writing of supporters of the portfolio model suggests that the approach is expensive to implement and may have negative effects on student achievement.In light of these considerations, it is recommended that policymakers and administrators use caution in considering the portfolio district approach. It is also highly recommended that before adopting such a strategy, decision makers ask the following questions.What credible evidence do we have, or can we obtain, that suggests the portfolio model offers advantages compared to other reform models? What would those advantages be, when might they be expected to materialize, and howmight they be documented?If constituent elements of the model (such as charter schools and test-based accountability) have not produced advantages outside of portfolio systems, whatis the rationale for expecting improved outcomes as part of a portfolio system?What funding will be needed for startup, and where will it come from?What funding will be necessary for maintenance of the model? Where will continuation funds come from if startup funds expire and are not renewed?How will the cost/benefit ratio of the model be determined?What potential political and social conflicts seem possible? How will concerns of dissenting constituents be addressed

Alternating register automata on finite words and trees

We study alternating register automata on data words and data trees in relation to logics. A data word (resp. data tree) is a word (resp. tree) whose every position carries a label from a finite alphabet and a data value from an infinite domain. We investigate one-way automata with alternating control over data words or trees, with one register for storing data and comparing them for equality. This is a continuation of the study started by Demri, Lazic and Jurdzinski. From the standpoint of register automata models, this work aims at two objectives: (1) simplifying the existent decidability proofs for the emptiness problem for alternating register automata; and (2) exhibiting decidable extensions for these models. From the logical perspective, we show that (a) in the case of data words, satisfiability of LTL with one register and quantification over data values is decidable; and (b) the satisfiability problem for the so-called forward fragment of XPath on XML documents is decidable, even in the presence of DTDs and even of key constraints. The decidability is obtained through a reduction to the automata model introduced. This fragment contains the child, descendant, next-sibling and following-sibling axes, as well as data equality and inequality tests