7 research outputs found
On the Complexity of Computing the Profinite Closure of a Rational Language
International audienceThe profinite topology is used in rational languages classification. In particular, several important decidability problems, related to the Malcev product, reduce to the computation of the closure of a rational language in the profinite topology. It is known that given a rational language by a deterministic automaton, computing a deterministic automaton accepting its profinite closure can be done with an exponential upper bound. This paper is dedicated the study of a lower bound for this problem: we prove that in some cases, if the alphabet contains at least three letters, it requires an exponential time
Quantum computation with devices whose contents are never read
In classical computation, a "write-only memory" (WOM) is little more than an
oxymoron, and the addition of WOM to a (deterministic or probabilistic)
classical computer brings no advantage. We prove that quantum computers that
are augmented with WOM can solve problems that neither a classical computer
with WOM nor a quantum computer without WOM can solve, when all other resource
bounds are equal. We focus on realtime quantum finite automata, and examine the
increase in their power effected by the addition of WOMs with different access
modes and capacities. Some problems that are unsolvable by two-way
probabilistic Turing machines using sublogarithmic amounts of read/write memory
are shown to be solvable by these enhanced automata.Comment: 32 pages, a preliminary version of this work was presented in the 9th
International Conference on Unconventional Computation (UC2010
Transitive Closures of Semi-commutation Relations on Regular omega-Languages
A semi-commutation is a relation on a finite alphabet . Given an infinite word on , we denote by and by the language . In this paper we prove that if an -language is a finite union of languages of the form , where the 's are subsets of the alphabet and the 's are letters, then is a computable regular -language accepting a similar decomposition. In addition we prove the same result holds for -languages which are finite unions of languages of the form , where the 's are accepted by diamond automata and the 's are letters. These results improve recent works by Bouajjani, Muscholl and Touili on one hand, and by Cécé, Héam and Mainier on the other hand, by extending them to infinite words
Sweeping Permutation Automata
This paper introduces sweeping permutation automata, which move over an input
string in alternating left-to-right and right-to-left sweeps and have a
bijective transition function. It is proved that these automata recognize the
same family of languages as the classical one-way permutation automata
(Thierrin, "Permutation automata", Mathematical Systems Theory, 1968). An
n-state two-way permutation automaton is transformed to a one-way permutation
automaton with F(n)=\max_(k+l=n, m <= l) k (l \choose m) (k - 1 \choose l - m)
(l - m)! states. This number of states is proved to be necessary in the worst
case, and its growth rate is estimated as F(n) = n^(n/2 - (1 + \ln 2)/2 \cdot
n/(\ln n) \cdot (1 + o(1))).Comment: In Proceedings NCMA 2023, arXiv:2309.0733
An Axiomatic Approach to Reversible Computation
Undoing computations of a concurrent system is beneficial inmany situations, e.g., in reversible debugging of multi-threaded programsand in recovery from errors due to optimistic execution in parallel dis-crete event simulation. A number of approaches have been proposed forhow to reverse formal models of concurrent computation including pro-cess calculi such as CCS, languages like Erlang, prime eventstructuresand occurrence nets. However it has not been settled what properties areversible system should enjoy, nor how the various properties that havebeen suggested, such as the parabolic lemma and the causal-consistencyproperty, are related. We contribute to a solution to these issues by usinga generic labelled transition system equipped with a relationcapturingwhether transitions are independent to explore the implications betweenthese properties. In particular, we show how they are derivable from aset of axioms. Our intention is that when establishing properties of someformalism it will be easier to verify the axioms rather than proving prop-erties such as the parabolic lemma directly. We also introduce two newnotions related to causal consistent reversibility, namely causal safetyand causal liveness, and show that they are derivable from our axioms
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.