Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTractability of Quantified Temporal Constraints To The Max
195
0
0.0
(
0
)
Added by
Micha{\\l} Wrona
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
A temporal constraint language is a set of relations that are first-order definable over (Q;<). We show that several temporal constraint languages whose constraint satisfaction problem is maximally tractable are also maximally tractable for the more expressive quantified constraint satisfaction problem. These constraint languages are defined in terms of preservation under certain binary polymorphisms. We also present syntactic characterizations of the relations in these languages.
rate research
Read More
The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for functional or imperative programs over algebraic data types such as lists and trees. However, as the theory of finite term algebras is not finitely axiomatizable, reasoning about quantified properties over term algebras is challenging. In this paper we address full first-order reasoning about properties of programs manipulating term algebras, and describe two approaches for doing so by using first-order theorem proving. Our first method is a conservative extension of the theory of term algebras using a finite number of statements, while our second method relies on extending the superposition calculus of first-order theorem provers with additional inference rules. We implemented our work in the first-order theorem prover Vampire and evaluated it on a large number of algebraic data type benchmarks, as well as game theory constraints. Our experimental results show that our methods are able to find proofs for many hard problems previously unsolved by state-of-the-art methods. We also show that Vampire implementing our methods outperforms existing SMT solvers able to deal with algebraic data types.
In temporal logics, a central question is about the choice of modalities and their relative expressive power, in comparison to the complexity of decision problems such as satisfiability. In this tutorial, we will illustrate the study of such questions over finite word models, first with logics for Unambiguous Starfree Regular Languages (UL), originally defined by Schutzenberger, and then for extensions with constraints, which appear in interval logics. We present Deterministic temporal logics, with diverse sets of modalities, which also characterize UL. The tools and techniques used go under the name of Turtle Programs or Rankers. These are simple kinds of automata. We use properties such as Ranker Directionality and Ranker Convexity to show that all these logics have NP satisfiability. A recursive extension of some of these modalities gives us the full power of first-order logic over finite linear orders. We also discuss Interval Constraint modalities extending Deterministic temporal logics, with intermediate expressiveness. These allow counting or simple algebraic operations on paths. The complexity of these extended logics is PSpace, as of full temporal logic (and ExpSpace when using binary notation).
We study quantified propositional logics from the complexity theoretic point of view. First we introduce alternating dependency quantified boolean formulae (ADQBF) which generalize both quantified and dependency quantified boolean formulae. We show that the truth evaluation for ADQBF is AEXPTIME(poly)-complete. We also identify fragments for which the problem is complete for the levels of the exponential hierarchy. Second we study propositional team-based logics. We show that DQBF formulae correspond naturally to quantified propositional dependence logic and present a general NEXPTIME upper bound for quantified propositional logic with a large class of generalized dependence atoms. Moreover we show AEXPTIME(poly)-completeness for extensions of propositional team logic with generalized dependence atoms.
Dependency quantified Boolean formulas (DQBFs) are a powerful formalism, which subsumes quantified Boolean formulas (QBFs) and allows an explicit specification of dependencies of existential variables on universal variables. Driven by the needs of various applications which can be encoded by DQBFs in a natural, compact, and elegant way, research on DQBF solving has emerged in the past few years. However, research focused on closed DQBFs in prenex form (where all quantifiers are placed in front of a propositional formula), while non-prenex DQBFs have almost not been studied in the literature. In this paper, we provide a formal definition for syntax and semantics of non-closed non-prenex DQBFs and prove useful properties enabling quantifier localization. Moreover, we make use of our theory by integrating quantifier localization into a state-of-the-art DQBF solver. Experiments with prenex DQBF benchmarks, including all instances from the QBFEVAL18-20 competitions, clearly show that quantifier localization pays off in this context.
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field of knowledge representation. We will also show that the decision problem for our language has a non-deterministic exponential time complexity. However, for the restricted case of formulae whose quantifier prefixes have length bounded by a constant, the decision problem becomes NP-complete. We also observe that in spite of such restriction, several useful set-theoretic constructs, mostly related to maps, are expressible. Finally, we present some undecidable extensions of our language, involving any of the operators domain, range, image, and map composition. [4] Michael Breban, Alfredo Ferro, Eugenio G. Omodeo and Jacob T. Schwartz (1981): Decision procedures for elementary sublanguages of set theory. II. Formulas involving restricted quantifiers, together with ordinal, integer, map, and domain notions. Communications on Pure and Applied Mathematics 34, pp. 177-195
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
