Ordered Navigation on Multi-attributed Data Words

Decker, Normann; Habermehl, Peter; Leucker, Martin; Thoma, Daniel

doi:10.1007/978-3-662-44584-6_34

Cited by 23 publications

(42 citation statements)

References 27 publications

(63 reference statements)

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“…These are finite words in which every position carries a label from a finite alphabet and a finite tuple of data values from some infinite alphabet. A wealth of specification formalisms for data words (and slight variants) have been introduced stemming from automata to adequate logical languages such as first-order logic [Bojańczyk et al 2011;Schwentick and Zeume 2012] and temporal logics [Figueira 2010;Decker et al 2014].…”

Section: Encoding Data Words With Multiple Attributesmentioning

confidence: 99%

Two-Variable Separation Logic and Its Inner Circle

Demri

Deters

2015

ACM Trans. Comput. Logic

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Separation logic is a well-known assertion language for Hoare-style proof systems. We show that first-order separation logic with a unique record field restricted to two quantified variables and no program variables is undecidable. This is among the smallest fragments of separation logic known to be undecidable, and this contrasts with the decidability of two-variable first-order logic. We also investigate its restriction by dropping the magic wand connective, known to be decidable with nonelementary complexity, and we show that the satisfiability problem with only two quantified variables is not yet elementary recursive. Furthermore, we establish insightful and concrete relationships between two-variable separation logic and propositional interval temporal logic (PITL), data logics, and modal logics, providing an inner circle of closely related logics.

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Section: Encoding Data Words With Multiple Attributesmentioning

confidence: 99%

Two-Variable Separation Logic and Its Inner Circle

Demri

Deters

2015

ACM Trans. Comput. Logic

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“…These cases can, however, be handled by additional constraints added to ϕ. Data words over a thus obtained partially ordered attribute set of depth k can now be encoded into words over the linear ordering [k] of equal depth k. The idea is to encode a single position into a frame of positions in the fashion of [KSZ10, DHLT14]. That way a single attribute on every level suffices.…”

Section: From Ltl ↓ Tqo To Ncs and Backmentioning

confidence: 99%

On Freeze LTL with Ordered Attributes

Decker

Thoma

2016

Lecture Notes in Computer Science

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This paper is concerned with Freeze LTL, a temporal logic on data words with registers. In a (multi-attributed) data word each position carries a letter from a finite alphabet and assigns a data value to a fixed, finite set of attributes. The satisfiability problem of Freeze LTL is undecidable if more than one register is available or tuples of data values can be stored and compared arbitrarily. Starting from the decidable one-register fragment we propose an extension that allows for specifying a dependency relation on attributes. This restricts in a flexible way how collections of attribute values can be stored and compared. This conceptual dimension is orthogonal to the number of registers or the available temporal operators. The extension is strict. Admitting arbitrary dependency relations, satisfiability becomes undecidable. Tree-like relations, however, induce a family of decidable fragments escalating the ordinal-indexed hierarchy of fast-growing complexity classes, a recently introduced framework for non-primitive recursive complexities. This results in completeness for the class Fε 0 . We employ nested counter systems and show that they relate to the hierarchy in terms of the nesting depth.

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“…PLRV LRV PLRV = CLTL XF,XF −1 [DDG12] LRV = CLTL XF [DDG12] (1 attribute) Figure 1: Placing LRV and variants in the family of data logics two fragments BD-LTL − and BD-LTL + of that richer logic have been introduced and shown to admit 2expspace-complete satisfiability problems. Forthcoming logic LRV is shown in [DHLT14] to be strictly less expressive than BD-LTL + .…”

Section: Introductionmentioning

confidence: 99%

“…Note that in [KSZ10], a richer logic BD-LTL has been introduced and it has been shown that satisfiability is equivalent to the reachability problem for Petri nets. Moreover, in [DHLT14], BD-LTL [KSZ10] (≡ Reach(VASS)) LTL ↓ 1 (X, X −1 , U, S) [DL09] (undec.) PLRV LRV PLRV = CLTL XF,XF −1 [DDG12] LRV = CLTL XF [DDG12] (1 attribute) Figure 1: Placing LRV and variants in the family of data logics two fragments BD-LTL − and BD-LTL + of that richer logic have been introduced and shown to admit 2expspace-complete satisfiability problems.…”

Section: Introductionmentioning

confidence: 99%

Reasoning about Data Repetitions with Counter Systems

Demri¹,

Figueira²,

Praveen³

2016

Logical Methods in Computer Science

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Abstract. We study linear-time temporal logics interpreted over data words with multiple attributes. We restrict the atomic formulas to equalities of attribute values in successive positions and to repetitions of attribute values in the future or past. We demonstrate correspondences between satisfiability problems for logics and reachability-like decision problems for counter systems. We show that allowing/disallowing atomic formulas expressing repetitions of values in the past corresponds to the reachability/coverability problem in Petri nets. This gives us 2expspace upper bounds for several satisfiability problems. We prove matching lower bounds by reduction from a reachability problem for a newly introduced class of counter systems. This new class is a succinct version of vector addition systems with states in which counters are accessed via pointers, a potentially useful feature in other contexts. We strengthen further the correspondences between data logics and counter systems by characterizing the complexity of fragments, extensions and variants of the logic. For instance, we precisely characterize the relationship between the number of attributes allowed in the logic and the number of counters needed in the counter system.

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Ordered Navigation on Multi-attributed Data Words

Cited by 23 publications

References 27 publications

Two-Variable Separation Logic and Its Inner Circle

Two-Variable Separation Logic and Its Inner Circle

On Freeze LTL with Ordered Attributes

Reasoning about Data Repetitions with Counter Systems

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