2,546 research outputs found
On Modal Logics of Partial Recursive Functions
The classical propositional logic is known to be sound and complete with
respect to the set semantics that interprets connectives as set operations. The
paper extends propositional language by a new binary modality that corresponds
to partial recursive function type constructor under the above interpretation.
The cases of deterministic and non-deterministic functions are considered and
for both of them semantically complete modal logics are described and
decidability of these logics is established
An Automata Theoretic Approach to the Zero-One Law for Regular Languages: Algorithmic and Logical Aspects
A zero-one language L is a regular language whose asymptotic probability
converges to either zero or one. In this case, we say that L obeys the zero-one
law. We prove that a regular language obeys the zero-one law if and only if its
syntactic monoid has a zero element, by means of Eilenberg's variety theoretic
approach. Our proof gives an effective automata characterisation of the
zero-one law for regular languages, and it leads to a linear time algorithm for
testing whether a given regular language is zero-one. In addition, we discuss
the logical aspects of the zero-one law for regular languages.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
Synthesis of Deterministic Top-down Tree Transducers from Automatic Tree Relations
We consider the synthesis of deterministic tree transducers from automaton
definable specifications, given as binary relations, over finite trees. We
consider the case of specifications that are deterministic top-down tree
automatic, meaning the specification is recognizable by a deterministic
top-down tree automaton that reads the two given trees synchronously in
parallel. In this setting we study tree transducers that are allowed to have
either bounded delay or arbitrary delay. Delay is caused whenever the
transducer reads a symbol from the input tree but does not produce output. We
provide decision procedures for both bounded and arbitrary delay that yield
deterministic top-down tree transducers which realize the specification for
valid input trees. Similar to the case of relations over words, we use
two-player games to obtain our results.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Noise-based information processing: Noise-based logic and computing: what do we have so far?
We briefly introduce noise-based logic. After describing the main motivations
we outline classical, instantaneous (squeezed and non-squeezed), continuum,
spike and random-telegraph-signal based schemes with applications such as
circuits that emulate the brain functioning and string verification via a slow
communication channel.Comment: Invited talk at the 21st International Conference on Noise and
Fluctuations, Toronto, Canada, June 12-16, 201
Sequent and Hypersequent Calculi for Abelian and Lukasiewicz Logics
We present two embeddings of infinite-valued Lukasiewicz logic L into Meyer
and Slaney's abelian logic A, the logic of lattice-ordered abelian groups. We
give new analytic proof systems for A and use the embeddings to derive
corresponding systems for L. These include: hypersequent calculi for A and L
and terminating versions of these calculi; labelled single sequent calculi for
A and L of complexity co-NP; unlabelled single sequent calculi for A and L.Comment: 35 pages, 1 figur
- …