784 research outputs found
Unified Analysis of Collapsible and Ordered Pushdown Automata via Term Rewriting
We model collapsible and ordered pushdown systems with term rewriting, by
encoding higher-order stacks and multiple stacks into trees. We show a uniform
inverse preservation of recognizability result for the resulting class of term
rewriting systems, which is obtained by extending the classic saturation-based
approach. This result subsumes and unifies similar analyses on collapsible and
ordered pushdown systems. Despite the rich literature on inverse preservation
of recognizability for term rewrite systems, our result does not seem to follow
from any previous study.Comment: in Proc. of FRE
On the descriptional complexity of iterative arrays
The descriptional complexity of iterative arrays (lAs) is studied. Iterative arrays are a parallel computational model with a sequential processing of the input. It is shown that lAs when compared to deterministic finite automata or pushdown automata may provide savings in size which are not bounded by any recursive function, so-called non-recursive trade-offs. Additional non-recursive trade-offs are proven to exist between lAs working in linear time and lAs working in real time. Furthermore, the descriptional complexity of lAs is compared with cellular automata (CAs) and non-recursive trade-offs are proven between two restricted classes. Finally, it is shown that many decidability questions for lAs are undecidable and not semidecidable
The Parametric Ordinal-Recursive Complexity of Post Embedding Problems
Post Embedding Problems are a family of decision problems based on the
interaction of a rational relation with the subword embedding ordering, and are
used in the literature to prove non multiply-recursive complexity lower bounds.
We refine the construction of Chambart and Schnoebelen (LICS 2008) and prove
parametric lower bounds depending on the size of the alphabet.Comment: 16 + vii page
Complexity Hierarchies Beyond Elementary
We introduce a hierarchy of fast-growing complexity classes and show its
suitability for completeness statements of many non elementary problems. This
hierarchy allows the classification of many decision problems with a
non-elementary complexity, which occur naturally in logic, combinatorics,
formal languages, verification, etc., with complexities ranging from simple
towers of exponentials to Ackermannian and beyond.Comment: Version 3 is the published version in TOCT 8(1:3), 2016. I will keep
updating the catalogue of problems from Section 6 in future revision
Bisimulation Equivalence of First-Order Grammars is ACKERMANN-Complete
Checking whether two pushdown automata with restricted silent actions are
weakly bisimilar was shown decidable by S\'enizergues (1998, 2005). We provide
the first known complexity upper bound for this famous problem, in the
equivalent setting of first-order grammars. This ACKERMANN upper bound is
optimal, and we also show that strong bisimilarity is primitive-recursive when
the number of states of the automata is fixed
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