Dynamic Complexity of Formal Languages

The paper investigates the power of the dynamic complexity classes DynFO, DynQF and DynPROP over string languages. The latter two classes contain problems that can be maintained using quantifier-free first-order updates, with and without auxiliary functions, respectively. It is shown that the languages maintainable in DynPROP exactly are the regular languages, even when allowing arbitrary precomputation. This enables lower bounds for DynPROP and separates DynPROP from DynQF and DynFO. Further, it is shown that any context-free language can be maintained in DynFO and a number of specific context-free languages, for example all Dyck-languages, are maintainable in DynQF. Furthermore, the dynamic complexity of regular tree languages is investigated and some results concerning arbitrary structures are obtained: there exist first-order definable properties which are not maintainable in DynPROP. On the other hand any existential first-order property can be maintained in DynQF when allowing precomputation.Comment: Contains the material presenten at STACS 2009, extendes with proofs and examples which were omitted due lack of spac

Complexity and composition of synthesized web services

The paper investigates fundamental decision problems and composition synthesis for Web services commonly found in practice. We propose a notion of synthesized Web services (SWS’s) to specify the behaviors of the services. Upon receiving a sequence of input messages, an SWS issues multiple queries to a database and generates actions, in parallel; it produces external messages and database updates by synthesizing the actions parallelly generated. In contrast to previous models for Web services, SWS’s advocate parallel processing and (deterministic) synthesis of actions. We classify SWS’s based on what queries an SWS can issue, how the synthesis of actions is expressed, and whether unbounded input sequences are allowed in a single interaction session. We show that the behaviors of Web services supported by various prior models, data-driven or not, can be specified by different SWS classes. For each of these classes we study the non-emptiness, validation and equivalence problems, and establish matching upper and lower bounds on these problems. We also provide complexity bounds on composition synthesis for these SWS classes, identifying decidable cases

Succinctness of pattern-based schema languages for XML

Martens et al. defined a pattern-based specification language equivalent in expressive power to the widely adopted XML Schema definitions (XSDs). This language consists of rules of the form (r, s) where r and s are regular expressions and can be seen as a type-free extension of DTDs with vertical regular expressions. Sets of such rules can be interpreted both in an existential or universal way. In the present paper, we study the succinctness of both semantics w.r.t. each other and w.r.t. the common abstraction of XSDs in terms of single-type extended DTDs. The investigation is carried out relative to three kinds of vertical pattern languages: regular, linear, and strongly linear patterns. We also consider the complexity of the simplification problem for each of the considered pattern-based schemas

SUCCINCTNESS OF THE COMPLEMENT AND INTERSECTION OF REGULAR EXPRESSIONS

We study the succinctness of the complement and intersection of regular expressions. In particular, we show that when constructing a regular expression defining the complement of a given regular expression, a double exponential size increase cannot be avoided. Similarly, when constructing a regular expression defining the intersection of a fixed and an arbitrary number of regular expressions, an exponential and double exponential size increase, respectively, can in worst-case not be avoided. All mentioned lower bounds improve the existing ones by one exponential and are tight in the sense that the target expression can be constructed in the corresponding time class, i.e., exponential or double exponential time. As a by-product, we generalize a theorem by Ehrenfeucht and Zeiger stating that there is a class of DFAs which are exponentially more succinct than regular expressions, to a fixed four-letter alphabet. When the given regular expressions are one-unambiguous, as for instance required by the XML Schema specification, the complement can be computed in polynomial time whereas the bounds concerning intersection continue to hold. For the subclass of single-occurrence regular expressions, we prove a tight exponential lower bound for intersection

Succinctness of pattern-based schema languages for XML

Abstract. Martens et al. defined a pattern-based specification language equivalent in expressive power to the widely adopted XML Schema definitions (XSDs). This language consists of rules of the form (r, s) where r and s are regular expressions and can be seen as a type-free extension of DTDs with vertical regular expressions. Sets of such rules can be interpreted both in an existential or universal way. In the present paper, we study the succinctness of both semantics w.r.t. each other and w.r.t. the common abstraction of XSDs in terms of single-type extended DTDs. The investigation is carried out relative to three kinds of vertical pattern languages: regular, linear, and strongly linear patterns. We also consider the complexity of the simplification problem for each of the considered pattern-based schema’s.