scholarly journals Unresolved systems of language equations: Expressive power and decision problems

2005 ◽  
Vol 349 (3) ◽  
pp. 283-308 ◽  
Author(s):  
Alexander Okhotin
Keyword(s):  
Expressive Power ◽  
Decision Problems ◽  
Language Equations

scholarly journals Document Spanners: From Expressive Power to Decision Problems

2017 ◽  
Vol 62 (4) ◽  
pp. 854-898 ◽  
Author(s):  
Dominik D. Freydenberger ◽  
Mario Holldack
Keyword(s):  
Expressive Power ◽  
Decision Problems

Site-directed insertion: Language equations and decision problems

2019 ◽  
Vol 798 ◽  
pp. 40-51
Author(s):  
Da-Jung Cho ◽  
Yo-Sub Han ◽  
Kai Salomaa ◽  
Taylor J. Smith
Keyword(s):  
Decision Problems ◽  
Language Equations

scholarly journals Pure-Past Linear Temporal and Dynamic Logic on Finite Traces

2020 ◽  
Author(s):  
Giuseppe De Giacomo ◽  
Antonio Di Stasio ◽  
Francesco Fuggitti ◽  
Sasha Rubin
Keyword(s):  
Decision Making ◽  
Dynamic Logic ◽  
Expressive Power ◽  
Decision Problems ◽  
Sequential Decision Making ◽  
Sequential Decision ◽  
The Past ◽  
Temporal Specifications

We review PLTLf and PLDLf, the pure-past versions of the well-known logics on finite traces LTLf and LDLf, respectively. PLTLf and PLDLf are logics about the past, and so scan the trace backwards from the end towards the beginning. Because of this, we can exploit a foundational result on reverse languages to get an exponential improvement, over LTLf /LDLf , for computing the corresponding DFA. This exponential improvement is reflected in several forms of sequential decision making involving temporal specifications, such as planning and decision problems in non-deterministic and non-Markovian domains. Interestingly, PLTLf (resp., PLDLf ) has the same expressive power as LTLf (resp., LDLf ), but transforming a PLTLf (resp., PLDLf ) formula into its equivalent LTLf (resp.,LDLf) is quite expensive. Hence, to take advantage of the exponential improvement, properties of interest must be directly expressed in PLTLf /PLDLf .

scholarly journals Language equations with complementation: Expressive power

2012 ◽  
Vol 416 ◽  
pp. 71-86 ◽  
Author(s):  
Alexander Okhotin ◽  
Oksana Yakimova
Keyword(s):  
Expressive Power ◽  
Language Equations

scholarly journals Decision problems for language equations

2010 ◽  
Vol 76 (3-4) ◽  
pp. 251-266 ◽  
Author(s):  
Alexander Okhotin
Keyword(s):  
Decision Problems ◽  
Language Equations

scholarly journals Language equations with complementation: Decision problems

2007 ◽  
Vol 376 (1-2) ◽  
pp. 112-126 ◽  
Author(s):  
Alexander Okhotin ◽  
Oksana Yakimova
Keyword(s):  
Decision Problems ◽  
Language Equations

A CHARACTERIZATION OF THE ARITHMETICAL HIERARCHY BY LANGUAGE EQUATIONS

2005 ◽  
Vol 16 (05) ◽  
pp. 985-998 ◽  
Author(s):  
ALEXANDER OKHOTIN
Keyword(s):  
Expressive Power ◽  
Peano Arithmetic ◽  
Extremal Solution ◽  
Boolean Operations ◽  
Arithmetical Hierarchy ◽  
First Order ◽  
Language Equations ◽  
Order Arithmetic

Language equations with all Boolean operations and concatenation and a particular order on the set of solutions are proved to be equal in expressive power to the first-order Peano arithmetic. In particular, it is shown that the class of sets representable using k variables (for every k ≥ 2) is exactly the k-th level of the arithmetical hierarchy, i.e., the sets definable by recursive predicates with k alternating quantifiers. The property of having an extremal solution is shown to be nonrepresentable in first-order arithmetic.

Bipolar Abstract Argumentation with Dual Attacks and Supports

2020 ◽  
Author(s):  
Nico Potyka
Keyword(s):  
Computational Complexity ◽  
Decision Problems ◽  
Abstract Argumentation ◽  
Stable Semantics ◽  
Support Relations ◽  
Support Relationships ◽  
Computational Properties ◽  
Inherent Tendency

Bipolar abstract argumentation frameworks allow modeling decision problems by defining pro and contra arguments and their relationships. In some popular bipolar frameworks, there is an inherent tendency to favor either attack or support relationships. However, for some applications, it seems sensible to treat attack and support equally. Roughly speaking, turning an attack edge into a support edge, should just invert its meaning. We look at a recently introduced bipolar argumentation semantics and two novel alternatives and discuss their semantical and computational properties. Interestingly, the two novel semantics correspond to stable semantics if no support relations are present and maintain the computational complexity of stable semantics in general bipolar frameworks.

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