4,772 research outputs found
Ambiguity, nondeterminism and state complexity of finite automata
The degree of ambiguity counts the number of accepting computations of a nondeterministic finite automaton (NFA) on a given input. Alternatively, the nondeterminism of an NFA can be measured by counting the amount of guessing in a single computation or the number of leaves of the computation tree on a given input. This paper surveys work on the degree of ambiguity and on various nondeterminism measures for finite automata. In particular, we focus on state complexity comparisons between NFAs with quantified ambiguity or nondeterminism
On finitely ambiguous B\"uchi automata
Unambiguous B\"uchi automata, i.e. B\"uchi automata allowing only one
accepting run per word, are a useful restriction of B\"uchi automata that is
well-suited for probabilistic model-checking. In this paper we propose a more
permissive variant, namely finitely ambiguous B\"uchi automata, a
generalisation where each word has at most accepting runs, for some fixed
. We adapt existing notions and results concerning finite and bounded
ambiguity of finite automata to the setting of -languages and present a
translation from arbitrary nondeterministic B\"uchi automata with states to
finitely ambiguous automata with at most states and at most accepting
runs per word
Infinite games with finite knowledge gaps
Infinite games where several players seek to coordinate under imperfect
information are deemed to be undecidable, unless the information is
hierarchically ordered among the players.
We identify a class of games for which joint winning strategies can be
constructed effectively without restricting the direction of information flow.
Instead, our condition requires that the players attain common knowledge about
the actual state of the game over and over again along every play.
We show that it is decidable whether a given game satisfies the condition,
and prove tight complexity bounds for the strategy synthesis problem under
-regular winning conditions given by parity automata.Comment: 39 pages; 2nd revision; submitted to Information and Computatio
Analyzing Catastrophic Backtracking Behavior in Practical Regular Expression Matching
We develop a formal perspective on how regular expression matching works in
Java, a popular representative of the category of regex-directed matching
engines. In particular, we define an automata model which captures all the
aspects needed to study such matching engines in a formal way. Based on this,
we propose two types of static analysis, which take a regular expression and
tell whether there exists a family of strings which makes Java-style matching
run in exponential time.Comment: In Proceedings AFL 2014, arXiv:1405.527
The finiteness of a group generated by a 2-letter invertible-reversible Mealy automaton is decidable
We prove that a semigroup generated by a reversible two-state Mealy automaton
is either finite or free of rank 2. This fact leads to the decidability of
finiteness for groups generated by two-state or two-letter
invertible-reversible Mealy automata and to the decidability of freeness for
semigroups generated by two-state invertible-reversible Mealy automata
Efficient Tabular LR Parsing
We give a new treatment of tabular LR parsing, which is an alternative to
Tomita's generalized LR algorithm. The advantage is twofold. Firstly, our
treatment is conceptually more attractive because it uses simpler concepts,
such as grammar transformations and standard tabulation techniques also know as
chart parsing. Secondly, the static and dynamic complexity of parsing, both in
space and time, is significantly reduced.Comment: 8 pages, uses aclap.st
- …