105 research outputs found
On state-alternating context-free grammars
AbstractState-alternating context-free grammars are introduced, and the language classes obtained from them are compared to the classes of the Chomsky hierarchy as well as to some well-known complexity classes. In particular, state-alternating context-free grammars are compared to alternating context-free grammars (Theoret. Comput. Sci. 67 (1989) 75–85) and to alternating pushdown automata. Further, various derivation strategies are considered, and their influence on the expressive power of (state-) alternating context-free grammars is investigated
Timed pushdown automata revisited
This paper contains two results on timed extensions of pushdown automata
(PDA). As our first result we prove that the model of dense-timed PDA of
Abdulla et al. collapses: it is expressively equivalent to dense-timed PDA with
timeless stack. Motivated by this result, we advocate the framework of
first-order definable PDA, a specialization of PDA in sets with atoms, as the
right setting to define and investigate timed extensions of PDA. The general
model obtained in this way is Turing complete. As our second result we prove
NEXPTIME upper complexity bound for the non-emptiness problem for an expressive
subclass. As a byproduct, we obtain a tight EXPTIME complexity bound for a more
restrictive subclass of PDA with timeless stack, thus subsuming the complexity
bound known for dense-timed PDA.Comment: full technical report of LICS'15 pape
Cost Automata, Safe Schemes, and Downward Closures
Higher-order recursion schemes are an expressive formalism used to define languages of possibly infinite ranked trees. They extend regular and context-free grammars, and are equivalent to simply typed ?Y-calculus and collapsible pushdown automata. In this work we prove, under a syntactical constraint called safety, decidability of the model-checking problem for recursion schemes against properties defined by alternating B-automata, an extension of alternating parity automata for infinite trees with a boundedness acceptance condition. We then exploit this result to show how to compute downward closures of languages of finite trees recognized by safe recursion schemes
08171 Abstracts Collection -- Beyond the Finite: New Challenges in Verification and Semistructured Data
From 20.04. to 25.04.2008, the Dagstuhl Seminar 08171 ``Beyond the Finite: New Challenges in Verification and Semistructured Data\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Domains for Higher-Order Games
We study two-player inclusion games played over word-generating higher-order
recursion schemes. While inclusion checks are known to capture verification
problems, two-player games generalize this relationship to program synthesis.
In such games, non-terminals of the grammar are controlled by opposing players.
The goal of the existential player is to avoid producing a word that lies
outside of a regular language of safe words.
We contribute a new domain that provides a representation of the winning
region of such games. Our domain is based on (functions over) potentially
infinite Boolean formulas with words as atomic propositions. We develop an
abstract interpretation framework that we instantiate to abstract this domain
into a domain where the propositions are replaced by states of a finite
automaton. This second domain is therefore finite and we obtain, via standard
fixed-point techniques, a direct algorithm for the analysis of two-player
inclusion games. We show, via a second instantiation of the framework, that our
finite domain can be optimized, leading to a (k+1)EXP algorithm for order-k
recursion schemes. We give a matching lower bound, showing that our approach is
optimal. Since our approach is based on standard Kleene iteration, existing
techniques and tools for fixed-point computations can be applied.Comment: Conference version accepted for presentation and publication at the
42nd International Symposium on Mathematical Foundations of Computer Science
(MFCS 2017
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