Backdoors for Linear Temporal Logic

Meier, Arne; Ordyniak, Sebastian; Ramanujan, M. S.; Schindler, Irena

doi:10.1007/s00453-018-0515-5

Cited by 5 publications

(4 citation statements)

References 41 publications

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“…When it was firstly introduced, the concept was defined with respect to CNF formulas of propositional logic. Yet, it has been transferred to different kind of logics and other areas as well: abduction [42], answer set programming [21,22], argumentation [17], default logic [20], temporal logic [40], planning [35], and constraint satisfaction [25]. For dependence logic, such a formalism does not exist so far.…”

Section: Resultsmentioning

confidence: 99%

Parameterised complexity of model checking and satisfiability in propositional dependence logic

Mahmood

Meier

2021

Ann Math Artif Intell

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Dependence Logic was introduced by Jouko Väänänen in 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parameterisations with respect to central decision problems. The model checking problem (MC) of PDL is NP-complete (Ebbing and Lohmann, SOFSEM 2012). The subject of this research is to identify a list of parameterisations (formula-size, formula-depth, treewidth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) which classically is known to be NP-complete as well (Lohmann and Vollmer, Studia Logica 2013). There we are presenting a different picture: under team-size, or dep-arity SAT is paraNP-complete whereas under all other mentioned parameters the problem is FPT. Finally, we introduce a variant of the satisfiability problem, asking for a team of a given size, and show for this problem an almost complete picture.

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Section: Resultsmentioning

confidence: 99%

Parameterised complexity of model checking and satisfiability in propositional dependence logic

Mahmood

Meier

2021

Ann Math Artif Intell

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“…This definition was first introduced by Golmes, Williams and Selman [18] to model short distances to efficient subclasses. Until today, backdoors gained copious attention in many different areas: abduction [33], answer set programming [34,35], argumentation [36], default logic [37], temporal logic [38], planning [39] and constraint satisfaction [40,41].…”

Section: Backdoorsmentioning

confidence: 99%

Parameterised Enumeration for Modification Problems

et al. 2019

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Recently, Creignou et al. (Theory Comput. Syst. 2017), introduced the class Delay FPT into parameterised complexity theory in order to capture the notion of efficiently solvable parameterised enumeration problems. In this paper, we propose a framework for parameterised ordered enumeration and will show how to obtain enumeration algorithms running with an FPT delay in the context of general modification problems. We study these problems considering two different orders of solutions, namely, lexicographic order and order by size. Furthermore, we present two generic algorithmic strategies. The first one is based on the well-known principle of self-reducibility and is used in the context of lexicographic order. The second one shows that the existence of a neighbourhood structure among the solutions implies the existence of an algorithm running with FPT delay which outputs all solutions ordered non-decreasingly by their size.

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“…This approach has been highly successful: applications can be found in e.g. (quantified) propositional satisfiability (Samer & Szeider, 2009a, 2009b, abductive reasoning (Pfandler, Rümmele, & Szeider, 2013), argumentation (Dvorák, Ordyniak, & Szeider, 2012), planning (Kronegger, Ordyniak, & Pfandler, 2019), logic (Meier, Ordyniak, Ramanujan, & Schindler, 2019), and answer set programming (Fichte & Szeider, 2015). Williams et al (2003) argue that backdoors may explain why SAT solvers occasionally fail to solve randomly generated instances with only a handful of variables but succeed in solving real-world instances containing thousands of variables.…”

Section: Introductionmentioning

confidence: 99%

“…This approach has been highly successful: applications can be found in e.g. (quantified) propositional satisfiability [49,50], abductive reasoning [46], argumentation [12], planning [37], logic [41], and answer set programming [15]. Williams et al (2003) argue that backdoors may explain why SAT solvers occasionally fail to solve randomly generated instances with only a handful of variables but succeed in solving real-world instances containing thousands of variables.…”

Section: Introductionmentioning

confidence: 99%

Computational Short Cuts in Infinite Domain Constraint Satisfaction

Jönsson¹,

Lagerkvist

Wang³

2022

jair

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A backdoor in a finite-domain CSP instance is a set of variables where each possible instantiation moves the instance into a polynomial-time solvable class. Backdoors have found many applications in artificial intelligence and elsewhere, and the algorithmic problem of finding such backdoors has consequently been intensively studied. Sioutis and Janhunen have proposed a generalised backdoor concept suitable for infinite-domain CSP instances over binary constraints. We generalise their concept into a large class of CSPs that allow for higher-arity constraints. We show that this kind of infinite-domain backdoors have many of the positive computational properties that finite-domain backdoors have: the associated computational problems are fixed parameter tractable whenever the underlying constraint language is finite. On the other hand, we show that infinite languages make the problems considerably harder: the general backdoor detection problem is W[2]-hard and fixed-parameter tractability is ruled out under standard complexity-theoretic assumptions. We demonstrate that backdoors may have suboptimal behaviour on binary constraints—this is detrimental from an AI perspective where binary constraints are predominant in, for instance, spatiotemporal applications. In response to this, we introduce sidedoors as an alternative to backdoors. The fundamental computational problems for sidedoors remain fixed-parameter tractable for finite constraint language (possibly also containing non-binary relations). Moreover, the sidedoor approach has appealing computational properties that sometimes leads to faster algorithms than the backdoor approach.

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Backdoors for Linear Temporal Logic

Cited by 5 publications

References 41 publications

Parameterised complexity of model checking and satisfiability in propositional dependence logic

Parameterised complexity of model checking and satisfiability in propositional dependence logic

Parameterised Enumeration for Modification Problems

Computational Short Cuts in Infinite Domain Constraint Satisfaction

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