Journal of the ACM

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Classical Descriptive Set Theory

We formalize and study business process systems that are centered around "business artifacts", or simply "artifacts". Artifacts are used to represent (real or conceptual) key business entities, including both their data schema and lifecycles. The lifecycle of an artifact type specifies the possible sequencings of services that can be applied to an artifact of this type as it progresses through the business process. The artifact-centric approach was introduced by IBM, and has been used to achieve substantial savings when performing business transformations.In this paper, artifacts carry attribute records and internal state relations (holding sets of tuples) that services can consult and update. In addition, services can access an underlying database and can introduce new values from an infinite domain, thus modeling external inputs or partially specified processes described by pre-and-post conditions. The lifecycles associate services to the artifacts using declarative, condition-action style rules.We consider the problem of statically verifying whether all runs of an artifact system satisfy desirable correctness properties expressed in a first-order extension of linear-time temporal logic. We map the boundaries of decidability for the verification problem and provide its complexity. The technical challenge to static verification stems from the presence of data from an infinite domain, yielding an infinite-state system. While much work has been done lately in the verification community on model checking specialized classes of infinite-state systems, the available results do not transfer to our framework, and this remains a difficult problem. We identify an expressive class of artifact systems for which verification is nonetheless decidable. The complexity of verification is PSPACE-complete, which is no worse than classical finite-state model checking.This investigation builds upon previous work on verification of data-driven Web services and ASM transducers, while addressing significant new technical challenges raised by the artifact model.

http://db.ucsd.edu/artifacts/pubs/324.pdf

Automatic verification of data-centric business processes

A data word is a sequence of pairs of a letter from a finite alphabet and an element from an infinite set, where the latter can only be compared for equality. To reason about data words, linear temporal logic is extended by the freeze quantifier, which stores the element at the current word position into a register, for equality comparisons deeper in the formula. By translations from the logic to alternating automata with registers and then to faulty counter automata whose counters may erroneously increase at any time, and from faulty and error-free counter automata to the logic, we obtain a complete complexity table for logical fragments defined by varying the set of temporal operators and the number of registers. In particular, the logic with future-time operators and 1 register is decidable but not primitive recursive over finite data words. Adding past-time operators or 1 more register, or switching to infinite data words, causes undecidability.

/pdf/ltl-with-the-freeze-quantifier-and-register-automata-je63a7e68g.pdf

LTL with the freeze quantifier and register automata

In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been already considered in the realm of semistructured data, timed automata and extended temporal logics. It is shown that satisfiability for the two-variable first-order logic FO^2(~,\le,+1) is decidable over finite and over infinite data words, where i« is a binary predicate testing the data value equality and +1,\le are the usual successor and order predicates. The complexity of the problem is at least as hard as Petri net reachability. Several extensions of the logic are considered, some remain decidable while some are undecidable.

/pdf/two-variable-logic-on-words-with-data-4c0cwhtbcj.pdf

Two-Variable Logic on Words with Data

In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. This model has been already considered in the realm of semistructured data, timed automata, and extended temporal logics.This article shows that satisfiability for the two-variable fragment FO2(∼,

/pdf/two-variable-logic-on-data-words-41h3uuqldq.pdf

Two-variable logic on data words

Motivated by reasoning tasks in the context of XML languages, the satisfiability problem of logics on data trees is investigated. The nodes of a data tree have a label from a finite set and a data value from a possibly infinite set. It is shown that satisfiability for two-variable first-order logic is decidable if the tree structure can be accessed only through the child and the next sibling predicates and the access to data values is restricted to equality tests. From this main result decidability of satisfiability and containment for a data-aware fragment of XPath and of the implication problem for unary key and inclusion constraints is concluded.

/pdf/two-variable-logic-on-data-trees-and-xml-reasoning-53ke4jb9i0.pdf

Two-variable logic on data trees and XML reasoning

Motivated by reasoning tasks for XML languages, the satisfiability problem of logics on data trees is investigated. The nodes of a data tree have a label from a finite set and a data value from a possibly infinite set. It is shown that satisfiability for two-variable first-order logic is decidable if the tree structure can be accessed only through the child and the next sibling predicates and the access to data values is restricted to equality tests. From this main result, decidability of satisfiability and containment for a data-aware fragment of XPath and of the implication problem for unary key and inclusion constraints is concluded.

/pdf/two-variable-logic-on-data-trees-and-xml-reasoning-500fctja74.pdf

We study languages over infinite alphabets equipped with some structure that
can be tested by recognizing automata. We develop a framework for studying such
alphabets and the ensuing automata theory, where the key role is played by an
automorphism group of the alphabet. In the process, we generalize nominal sets
due to Gabbay and Pitts.

/pdf/automata-theory-in-nominal-sets-27oec3ongm.pdf

Mikołaj Bojańczyk

Papers

Two-Variable Logic on Words with Data

Two-variable logic on data words

Two-variable logic on data trees and XML reasoning

Two-variable logic on data trees and XML reasoning

Automata theory in nominal sets