Decidable Classes of Tree Automata Mixing Local and Global Constraints Modulo Flat Theories

We define a class of ranked tree automata TABG generalizing both the tree automata with local tests between brothers of Bogaert and Tison (1992) and with global equality and disequality constraints (TAGED) of Filiot et al. (2007). TABG can test for equality and disequality modulo a given flat equational theory between brother subterms and between subterms whose positions are defined by the states reached during a computation. In particular, TABG can check that all the subterms reaching a given state are distinct. This constraint is related to monadic key constraints for XML documents, meaning that every two distinct positions of a given type have different values. We prove decidability of the emptiness problem for TABG. This solves, in particular, the open question of the decidability of emptiness for TAGED. We further extend our result by allowing global arithmetic constraints for counting the number of occurrences of some state or the number of different equivalence classes of subterms (modulo a given flat equational theory) reaching some state during a computation. We also adapt the model to unranked ordered terms. As a consequence of our results for TABG, we prove the decidability of a fragment of the monadic second order logic on trees extended with predicates for equality and disequality between subtrees, and cardinality.Comment: 39 pages, to appear in LMCS journa

{SAT} Solvers for Queries over Tree Automata with Constraints

International audienceTree automata turned out to be a very convenient framework for modeling and proving properties on infinite systems like communication protocols, Java programs and also in the context of XML programming. Unfortunately, these works are not always supported by efficient verification and validation tools. This paper investigates the use of two SAT solvers --- minisat and picosat--- to evaluate queries over tree automata with global equality and disequality constraints (TAGED s for short). Unlike general tree automata, TAGED s allow to express constraints useful for e.g., evaluating queries over XML documents, like "in the document, two nodes do not have the same key". These queries being based on the membership problem which is NP-complete for TAGEDs, we propose an efficient SAT encoding of the membership problem for TAGEDs and we show its correctness and soundness. The paper reports on the experimental results, and implementation details are given

The Emptiness Problem for Tree Automata with at Least One Disequality Constraint is NP-hard

The model of tree automata with equality and disequality constraints was introduced in 2007 by Filiot, Talbot and Tison. In this paper we show that if there is at least one disequality constraint, the emptiness problem is NP-hard

Rigid Tree Automata and Applications

International audienceWe introduce the class of Rigid Tree Automata (RTA), an extension of standard bottom-up automata on ranked trees with distinguished states called rigid. Rigid states define a restriction on the computation of RTA on trees: RTA can test for equality in subtrees reaching the same rigid state. RTA are able to perform local and global tests of equality between subtrees, non-linear tree pattern matching, and some inequality and disequality tests as well. Properties like determinism, pumping lemma, Boolean closure, and several decision problems are studied in detail. In particular, the emptiness problem is shown decidable in linear time for RTA whereas membership of a given tree to the language of a given RTA is NP-complete. Our main result is the decidability of whether a given tree belongs to the rewrite closure of an RTA language under a restricted family of term rewriting systems, whereas this closure is not an RTA language. This result, one of the first on rewrite closure of languages of tree automata with constraints, is enabling the extension of model checking procedures based on finite tree automata techniques, in particular for the verification of communicating processes with several local non rewritable memories, like security protocols. Finally, a comparison of RTA with several classes of tree automata with local and global equality tests, with dag automata and Horn clause formalisms is also provided

Tree automata with constraints and tree homomorphisms

Automata are a widely used formalism in computer science as a concise representation for sets. They are interesting from a theoretical and practical point of view. This work is focused on automata that are executed on tree-like structures, and thus, define sets of trees. Moreover, we tackle automata that are enhanced with the possibility to check (dis)equality constraints, i.e., where the automata are able to test whether specific subtrees of the input tree are equal or different. Two distinct mechanisms are considered for defining which subtrees have to be compared in the evaluation of the constraints. First, in local constraints, a transition of the automaton compares subtrees pending at positions relative to the position of the input tree where the transition takes place. Second, in global constraints, the subtrees tested are selected depending on the state to which they are evaluated by the automaton during a computation. In the setting of local constraints, we introduce tree automata with height constraints between brothers. These constraints are predicates on sibling subtrees that, instead of evaluating whether the subtrees are equal or different, compare their respective heights. Such constraints allow to express natural tree sets like complete or balanced (like AVL) trees. We prove decidability of emptiness and finiteness for these automata, and also for their combination with the tree automata with (dis)equality constraints between brothers of Bogaert and Tison (1992). We also define a new class of tree automata with constraints that allows arbitrary local disequality constraints and a particular kind of local equality constraints. We prove decidability of emptiness and finiteness for this class in exponential time. As a consequence, we obtain several EXPTIME-completeness results for problems on images of regular tree sets under tree homomorphisms, like set inclusion, finiteness of set difference, and regularity (also called HOM problem). In the setting of global constraints, we study the class of tree automata with global reflexive disequality constraints. Such kind of constraints is incomparable with the original notion of global disequality constraints of Filiot et al. (2007): the latter restricts disequality tests to only compare subtrees evaluated to distinct states, whereas in our model it is possible to test that all subtrees evaluated to the same given state are pairwise different. Our tests correspond to monadic key constraints, and thus, can be used to characterize unique identifiers, a typical integrity constraint of XML schemas. We study the emptiness and finiteness problems for these automata, and obtain decision algorithms that take triple exponential time.Los autómatas son un formalismo ampliamente usado en ciencias de la computación como una representación concisa para conjuntos, siendo interesantes tanto a nivel teórico como práctico. Este trabajo se centra en autómatas que se ejecutan en estructuras arbóreas, y por tanto, definen conjuntos de árboles. En particular, tratamos autómatas que han sido extendidos con la posibilidad de comprobar restricciones de (des)igualdad, es decir, autómatas que son capaces de comprobar si ciertos subárboles del árbol de entrada son iguales o diferentes. Se consideran dos mecanismos distintos para definir qué subárboles deben ser comparados en la evaluación de las restricciones. Primero, en las restricciones locales, una transición del autómata compara subárboles que penden en posiciones relativas a la posición del árbol de entrada en que se aplica la transición. Segundo, en restricciones globales, los subárboles comparados se seleccionan dependiendo del estado al que son evaluados por el autómata durante el cómputo. En el marco de restricciones locales, introducimos los autómatas de árboles con restricciones de altura entre hermanos. Estas restricciones son predicados entre subárboles hermanos que, en lugar de evaluar si los subárboles son iguales o diferentes, comparan sus respectivas alturas. Este tipo de restricciones permiten expresar conjuntos naturales de árboles, tales como árboles completos o equilibrados (como AVL). Demostramos la decidibilidad de la vacuidad y finitud para este tipo de autómata, y también para su combinación con los autómata con restricciones de (des)igualdad entre hermanos de Bogaert y Tison (1992). También definimos una nueva clase de autómatas con restricciones que permite restricciones locales de desigualdad arbitrarias y un tipo particular de restricciones locales de igualdad. Demostramos la decidibilidad de la vacuidad y finitud para esta clase, con un algoritmo de tiempo exponencial. Como consecuencia, obtenemos varios resultados de EXPTIME-completitud para problemas en imágenes de conjuntos regulares de árboles a través de homomorfismos de árboles, tales como inclusión de conjuntos, finitud de diferencia de conjuntos, y regularidad (también conocido como el problema HOM). En el marco de restricciones globales, estudiamos la clase de autómatas de árboles con restricciones globales de desigualdad reflexiva. Este tipo de restricciones es incomparable con la noción original de restricciones globales de desigualdad de Filiot et al. (2007): éstas últimas restringen las comprobaciones de desigualdad a subárboles que se evalúen a estados distintos, mientras que en nuestro modelo es posible comprobar que todos los subárboles que se evalúen a un mismo estado dado son dos a dos distintos. Nuestras restricciones corresponden a restricciones de clave, y por tanto, pueden ser usadas para caracterizar identificadores únicos, una restricción de integridad típica de los XML Schemas. Estudiamos los problemas de vacuidad y finitud para estos autómatas, y obtenemos algoritmos de decisión con coste temporal triplemente exponencial.Postprint (published version

Protecting the Protected Group: Circumventing Harmful Fairness

Machine Learning (ML) algorithms shape our lives. Banks use them to determine if we are good borrowers; IT companies delegate them recruitment decisions; police apply ML for crime-prediction, and judges base their verdicts on ML. However, real-world examples show that such automated decisions tend to discriminate against protected groups. This potential discrimination generated a huge hype both in media and in the research community. Quite a few formal notions of fairness were proposed, which take a form of constraints a "fair" algorithm must satisfy. We focus on scenarios where fairness is imposed on a self-interested party (e.g., a bank that maximizes its revenue). We find that the disadvantaged protected group can be worse off after imposing a fairness constraint. We introduce a family of \textit{Welfare-Equalizing} fairness constraints that equalize per-capita welfare of protected groups, and include \textit{Demographic Parity} and \textit{Equal Opportunity} as particular cases. In this family, we characterize conditions under which the fairness constraint helps the disadvantaged group. We also characterize the structure of the optimal \textit{Welfare-Equalizing} classifier for the self-interested party, and provide an algorithm to compute it. Overall, our \textit{Welfare-Equalizing} fairness approach provides a unified framework for discussing fairness in classification in the presence of a self-interested party.Comment: Published in AAAI 202

A project to investigate mechanisms and methodologies for the design and construction of communicating concurrent processes in real-time environments

Research undertaken in 1979 into effective and appropriate mechanisms to aid in the design and construction of software for use in the flight research programs undertaken by NASA is presented

Valence Advantages and Public Goods Consumption: Does a Disadvantaged Candidate Choose an Extremist Position?

Does a disadvantaged candidate always choose an extremist program? When does a less competent candidate have an incentive to move to extreme positions in order to differentiate himself from the more competent candidate? If the answer to these questions were positive, as suggested in recent work (Ansolabehere and Snyder (2000), Aragones and Palfrey (2002), Groseclose (1999), and Aragones and Palfrey (2003)), this would mean that extremist candidates are bad politicians. We consider a two candidates electoral competition over public consumption, with a two dimensional policy space and two dimensions of candidates heterogeneity. In this setting, we show that the conclusion depends on candidates relative competences over the two public goods and distinguish between two types of advantages (an absolute advantage and comparative advantage in providing the two public goods).Candidate Quality, Extremism, Public Goods Consumption

How Institutional Economics May Support the Analysis of Individual and Collective Capabilities

The analysis in this article starts from the recognition that institutions make an important part of the Capability Approach, as conversion factors from resources to capabilities and as affecting agency. The tradition of Old Institutional Economics is critical of the neoclassical view of the individual and agency and emphasises the importance of social context. Hence, there is some common ground between the Capability Approach (CA) and Old Institutional Economics (OIE). The purpose of this article is to explore how insights from OIE might enrich the CA both conceptually and empirically. This may be done for individual capabilities as well as for collective capabilities. A better understanding of collective resource-institutions and collective agency-institutions will also contribute to the analysis of capability expansion in the community economy through collective productive capabilities in commons, cooperatives and mutuals. The conclusion is that an understanding of institutions in the tradition of OIE may help to clarify the relationships between social norms and agency; complement the notion of constrained choice with enabling institutions; and point at how institutional transformation may support individual and collective capability expansion

How Institutional Economics May Support the Analysis of Individual and Collective Capabilities

The analysis in this article starts from the recognition that institutions make an important part of the Capability Approach, as conversion factors from resources to capabilities and as affecting agency. The tradition of Old Institutional Economics is critical of the neoclassical view of the individual and agency and emphasises the importance of social context. Hence, there is some common ground between the Capability Approach (CA) and Old Institutional Economics (OIE). The purpose of this article is to explore how insights from OIE might enrich the CA both conceptually and empirically. This may be done for individual capabilities as well as for collective capabilities. A better understanding of collective resource-institutions and collective agency-institutions will also contribute to the analysis of capability expansion in the community economy through collective productive capabilities in commons, cooperatives and mutuals. The conclusion is that an understanding of institutions in the tradition of OIE may help to clarify the relationships between social norms and agency; complement the notion of constrained choice with enabling institutions; and point at how institutional transformation may support individual and collective capability expansion