797 research outputs found
Visibly Linear Dynamic Logic
We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear
Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown
languages over finite words. In VLDL one can, e.g., express that a function
resets a variable to its original value after its execution, even in the
presence of an unbounded number of intermediate recursive calls. We prove that
VLDL describes exactly the -visibly pushdown languages. Thus it is
strictly more expressive than LTL and able to express recursive properties of
programs with unbounded call stacks.
The main technical contribution of this work is a translation of VLDL into
-visibly pushdown automata of exponential size via one-way alternating
jumping automata. This translation yields exponential-time algorithms for
satisfiability, validity, and model checking. We also show that visibly
pushdown games with VLDL winning conditions are solvable in triply-exponential
time. We prove all these problems to be complete for their respective
complexity classes.Comment: 25 Page
Deterministic regular functions of infinite words
Regular functions of infinite words are (partial) functions realized by
deterministic two-way transducers with infinite look-ahead. Equivalently, Alur
et. al. have shown that they correspond to functions realized by deterministic
Muller streaming string transducers, and to functions defined by
MSO-transductions. Regular functions are however not computable in general (for
a classical extension of Turing computability to infinite inputs), and we
consider in this paper the class of deterministic regular functions of infinite
words, realized by deterministic two-way transducers without look-ahead. We
prove that it is a well-behaved class of functions: they are computable, closed
under composition, characterized by the guarded fragment of MSO-transductions,
by deterministic B\"uchi streaming string transducers, by deterministic two-way
transducers with finite look-ahead, and by finite compositions of sequential
functions and one fixed basic function called map-copy-reverse.Comment: 45 page
One Theorem to Rule Them All: A Unified Translation of LTL into {\omega}-Automata
We present a unified translation of LTL formulas into deterministic Rabin
automata, limit-deterministic B\"uchi automata, and nondeterministic B\"uchi
automata. The translations yield automata of asymptotically optimal size
(double or single exponential, respectively). All three translations are
derived from one single Master Theorem of purely logical nature. The Master
Theorem decomposes the language of a formula into a positive boolean
combination of languages that can be translated into {\omega}-automata by
elementary means. In particular, Safra's, ranking, and breakpoint constructions
used in other translations are not needed
State-deterministic Finite Automata with Translucent Letters and Finite Automata with Nondeterministically Translucent Letters
Deterministic and nondeterministic finite automata with translucent letters
were introduced by Nagy and Otto more than a decade ago as Cooperative
Distributed systems of a kind of stateless restarting automata with window size
one. These finite state machines have a surprisingly large expressive power:
all commutative semi-linear languages and all rational trace languages can be
accepted by them including various not context-free languages. While the
nondeterministic variant defines a language class with nice closure properties,
the deterministic variant is weaker, however it contains all regular languages,
some non-regular context-free languages, as the Dyck language, and also some
languages that are not even context-free. In all those models for each state,
the letters of the alphabet could be in one of the following categories: the
automaton cannot see the letter (it is translucent), there is a transition
defined on the letter (maybe more than one transitions in nondeterministic
case) or none of the above categories (the automaton gets stuck by seeing this
letter at the given state and this computation is not accepting).
State-deterministic automata are recent models, where the next state of the
computation determined by the structure of the automata and it is independent
of the processed letters. In this paper our aim is twofold, on the one hand, we
investigate state-deterministic finite automata with translucent letters. These
automata are specially restricted deterministic finite automata with
translucent letters.
In the other novel model we present, it is allowed that for a state the set
of translucent letters and the set of letters for which transition is defined
are not disjoint. One can interpret this fact that the automaton has a
nondeterministic choice for each occurrence of such letters to see them (and
then erase and make the transition) or not to see that occurrence at that time.
Based on these semi-translucent letters, the expressive power of the automata
increases, i.e., in this way a proper generalization of the previous models is
obtained.Comment: In Proceedings AFL 2023, arXiv:2309.0112
Reversible Two-Party Computations
Deterministic synchronous systems consisting of two finite automata running
in opposite directions on a shared read-only input are studied with respect to
their ability to perform reversible computations, which means that the automata
are also backward deterministic and, thus, are able to uniquely step the
computation back and forth. We study the computational capacity of such devices
and obtain on the one hand that there are regular languages that cannot be
accepted by such systems. On the other hand, such systems can accept even
non-semilinear languages. Since the systems communicate by sending messages, we
consider also systems where the number of messages sent during a computation is
restricted. We obtain a finite hierarchy with respect to the allowed amount of
communication inside the reversible classes and separations to general, not
necessarily reversible, classes. Finally, we study closure properties and
decidability questions and obtain that the questions of emptiness, finiteness,
inclusion, and equivalence are not semidecidable if a superlogarithmic amount
of communication is allowed.Comment: In Proceedings AFL 2023, arXiv:2309.0112
Cyclic Proofs and Jumping Automata
We consider a fragment of a cyclic sequent proof system for Kleene algebra, and we see it as a computational device for recognising languages of words. The starting proof system is linear and we show that it captures precisely the regular languages. When adding the standard contraction rule, the expressivity raises significantly; we characterise the corresponding class of languages using a new notion of multi-head finite automata, where heads can jump
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