696 research outputs found
Non-termination using Regular Languages
We describe a method for proving non-looping non-termination, that is, of
term rewriting systems that do not admit looping reductions. As certificates of
non-termination, we employ regular (tree) automata.Comment: Published at International Workshop on Termination 201
Proving Looping and Non-Looping Non-Termination by Finite Automata
A new technique is presented to prove non-termination of term rewriting. The
basic idea is to find a non-empty regular language of terms that is closed
under rewriting and does not contain normal forms. It is automated by
representing the language by a tree automaton with a fixed number of states,
and expressing the mentioned requirements in a SAT formula. Satisfiability of
this formula implies non-termination. Our approach succeeds for many examples
where all earlier techniques fail, for instance for the S-rule from combinatory
logic
Synchronizing non-deterministic finite automata
In this paper, we show that every D3-directing CNFA can be mapped uniquely to
a DFA with the same synchronizing word length. This implies that \v{C}ern\'y's
conjecture generalizes to CNFAs and that the general upper bound for the length
of a shortest D3-directing word is equal to the Pin-Frankl bound for DFAs. As a
second consequence, for several classes of CNFAs sharper bounds are
established. Finally, our results allow us to detect all critical CNFAs on at
most 6 states. It turns out that only very few critical CNFAs exist.Comment: 21 page
Stream Productivity by Outermost Termination
Streams are infinite sequences over a given data type. A stream specification
is a set of equations intended to define a stream. A core property is
productivity: unfolding the equations produces the intended stream in the
limit. In this paper we show that productivity is equivalent to termination
with respect to the balanced outermost strategy of a TRS obtained by adding an
additional rule. For specifications not involving branching symbols
balancedness is obtained for free, by which tools for proving outermost
termination can be used to prove productivity fully automatically
Proving non-termination by finite automata
A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the language by a tree automaton with a fixed number of states, and expressing the mentioned requirements in a SAT formula. Satisfiability of this formula implies non-termination. Our approach succeeds for many examples where all earlier techniques fail, for instance for the S-rule from combinatory logic
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