scholarly journals Linear Game Automata: Decidable Hierarchy Problems for Stripped-Down Alternating Tree Automata

2009 ◽  
pp. 225-239 ◽  
Author(s):  
Jacques Duparc ◽  
Alessandro Facchini ◽  
Filip Murlak
Keyword(s):  
Tree Automata ◽  
Alternating Tree Automata ◽  
Hierarchy Problems

Church's Problem Revisited

1999 ◽  
Vol 5 (2) ◽  
pp. 245-263 ◽  
Author(s):  
Orna Kupferman ◽  
Moshe Y. Vardi
Keyword(s):  
Incomplete Information ◽  
Program Synthesis ◽  
Synthesis Problem ◽  
Tree Automata ◽  
Full Generality ◽  
Input Signals ◽  
Alternating Tree Automata ◽  
History Of ◽  
Underlying Processes

AbstractIn program synthesis, we transform a specification into a system that is guaranteed to satisfy the specification. When the system is open, then at each moment it reads input signals and writes output signals, which depend on the input signals and the history of the computation so far. The specification considers all possible input sequences. Thus, if the specification is linear, it should hold in every computation generated by the interaction, and if the specification is branching, it should hold in the tree that embodies all possible input sequences.Often, the system cannot read all the input signals generated by its environment. For example, in a distributed setting, it might be that each process can read input signals of only part of the underlying processes. Then, we should transform a specification into a system whose output depends only on the readable parts of the input signals and the history of the computation. This is called synthesis with incomplete information. In this work we solve the problem of synthesis with incomplete information in its full generality. We consider linear and branching settings with complete and incomplete information. We claim that alternation is a suitable and helpful mechanism for coping with incomplete information. Using alternating tree automata, we show that incomplete information does not make the synthesis problem more complex, in both the linear and the branching paradigm. In particular, we prove that independently of the presence of incomplete information, the synthesis problems for CTL and CTL*. are complete for EXPTIME and 2EXPTIME, respectively.

scholarly journals Monoidal-closed categories of tree automata

2020 ◽  
Vol 30 (1) ◽  
pp. 62-117
Author(s):  
Colin Riba
Keyword(s):  
Linear Logic ◽  
Tree Automata ◽  
Sequential Games ◽  
Infinite Trees ◽  
Alternating Tree Automata ◽  
Deduction Rules ◽  
New Perspective ◽  
Alternating Automata ◽  
Second Order Logic ◽  
Monadic Second Order Logic

AbstractThis paper surveys a new perspective on tree automata and Monadic second-order logic (MSO) on infinite trees. We show that the operations on tree automata used in the translations of MSO-formulae to automata underlying Rabin’s Tree Theorem (the decidability of MSO) correspond to the connectives of Intuitionistic Multiplicative Exponential Linear Logic (IMELL). Namely, we equip a variant of usual alternating tree automata (that we call uniform tree automata) with a fibered monoidal-closed structure which in particular handles a linear complementation of alternating automata. Moreover, this monoidal structure is actually Cartesian on non-deterministic automata, and an adaptation of a usual construction for the simulation of alternating automata by non-deterministic ones satisfies the deduction rules of the !(–) exponential modality of IMELL. (But this operation is unfortunately not a functor because it does not preserve composition.) Our model of IMLL consists in categories of games which are based on usual categories of two-player linear sequential games called simple games, and which generalize usual acceptance games of tree automata. This model provides a realizability semantics, along the lines of Curry–Howard proofs-as-programs correspondence, of a linear constructive deduction system for tree automata. This realizability semantics, which can be summarized with the slogan “automata as objects, strategies as morphisms,” satisfies an expected property of witness extraction from proofs of existential statements. Moreover, it makes it possible to combine realizers produced as interpretations of proofs with strategies witnessing (non-)emptiness of tree automata.

scholarly journals Alternating Tree Automata with Qualitative Semantics

2021 ◽  
Vol 22 (1) ◽  
pp. 1-24
Author(s):  
Raphaël Berthon ◽  
Nathanaël Fijalkow ◽  
Emmanuel Filiot ◽  
Shibashis Guha ◽  
Bastien Maubert ◽  
...  
Keyword(s):  
Tree Automata ◽  
Alternating Tree Automata
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