Undecidable boundedness problems for datalog programs

Hillebrand, Gerd G.; Kanellakis, Paris C.; Mairson, Harry G.; Vardi, Moshe Y.

doi:10.1016/0743-1066(95)00051-k

Cited by 44 publications

(30 citation statements)

References 12 publications

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“…The reduction is modified from the one used by Vardi et al [33,19] in proving the undecidability of boundedness for binary Datalog programs. We briefly describe their reduction and the changes below.…”

Section: Proofmentioning

confidence: 99%

Nonrecursive incremental evaluation of Datalog queries

Dong

Topor

1995

Ann Math Artif Intell

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We consider the problem of repeatedly evaluating the same (computationally expensive) query to a database that is being updated between successive query requests. In this situation, it should be possible to use the difference between successive database states and the answer to the query in one state to reduce the cost of evaluating the query in the next state. We use nonrecursive Datalog (which are unions of conjunctive queries) to compute the differences, and call this process "incremental query evaluation using conjunctive queries."After formalizing the notion of incremental query evaluation using conjunctive queries, we give an algorithm that constructs, for each regular chain query (including transitive closure as a special case), a nonrecursive Datalog program to compute the difference between the answer after an update and the answer before the update. We then extend this result to weakly regular queries, which are regular chain programs augmented with conjunctive queries having the so-called cartesian-closed increment property, and to the case of unbounded-set insertions where the sets are binary cartesian products. Finally, we show that the class of conjunctive queries with the cartesian-closed increment property is decidable.

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Section: Proofmentioning

confidence: 99%

Nonrecursive incremental evaluation of Datalog queries

Dong

Topor

1995

Ann Math Artif Intell

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“…We will prove the undecidability of the finiteness of forward closure by reduction from the uniform mortality problem for deterministic Turing machines [11]. Given a deterministic Turing machine M , the machine is said to be uniformly mortal if and only if there is a number k such that, for any instantaneous description I of M , the number of transitions that M can make starting from I is at most k.…”

Section: Undecidability Of Finiteness Of Forward Closurementioning

confidence: 99%

On Forward Closure and the Finite Variant Property

Bouchard

Gero

Lynch

et al. 2013

Frontiers of Combining Systems

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Abstract. Equational unification is an important research area with many applications, such as cryptographic protocol analysis. Unification modulo a convergent term rewrite system is undecidable, even with just a single rule. To identify decidable (and tractable) cases, two paradigms have been developed -Basic Syntactic Mutation [14] and the Finite Variant Property [6]. Inspired by the Basic Syntactic Mutation approach, we investigate the notion of forward closure along with suitable redundancy constraints. We show that a convergent term rewriting system R has a finite forward closure if and only if R has the finite variant property. We also show the undecidability of the finiteness of forward closure, therefore determining if a system has the finite variant property is undecidable.

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“…P if for each set D of edb facts T`+ Proof. The proof is based on a reduction using a similar technique as in [11]. (The reduction simulates the checking of whether the input database describes a halting configuration of a Turing machine starting from an empty tape.)…”

Section: U T 6 Decision Problems For Increment Boundednessmentioning

confidence: 99%

Increment boundedness and nonrecursive incremental evaluation of datalog queries

Dong

1995

Database Theory — ICDT '95

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Abstract. Given a recursive (datalog) query, the nonrecursive incremental evaluation approach uses nonrecursive (datalog) programs to compute the difference of the answers to the query against successive databases between updates. The mechanism used in this approach is called a "First-Order Incremental Evaluation System" (FOIES). We show that for two large classes of datalog queries, called "generalized (weakly) regular queries", FOIES always exist. We also define "increment boundedness" and its variations, which generalize boundedness. Increment bounded queries are shown to have FOIES of certain forms. We also relate increment boundedness to structural recursion, which was proposed for bulk data types. We characterize increment boundednessusing the "insertion idempotency", "insertion commutativity", and "determinism" properties of structural recursion. Finally, we show that the increment boundedness notions are undecidable and a decidable sufficient condition is given.

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Undecidable boundedness problems for datalog programs

Cited by 44 publications

References 12 publications

Nonrecursive incremental evaluation of Datalog queries

Nonrecursive incremental evaluation of Datalog queries

On Forward Closure and the Finite Variant Property

Increment boundedness and nonrecursive incremental evaluation of datalog queries

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