arXiv subjects

Andreas Maletti

Publications and source records attributed to Andreas Maletti.

16 recordsLinked to original sources

arXiv2026

Process-Mining of Hypertraces: Enabling Scalable Formal Security Verification of (Automotive) Network Architectures

The automotive domain is transitioning: vehicles act as rolling servers, persistently connected to numerous external entities. This connectivity, combined with rising on-board computing power for advanced driver assistance systems and similar use cases, creates escalating challenges for securing automotive network architectures. This work advances the security analysis of internet-connected automotive network architectures and their protocols. We introduce a strong, active adversary model tailored to the automotive domain. We substantially extend security protocol verification possible based on Attack Resilience Hyperproperties (ARHs) by introducing a verification-orchestration algorithm. Furthermore, we provide methods for comparative attribution of security property invalidations to specific, ne-grained component compromises. We present a novel integration of formal verification and process mining. By utilizing ARH counterexample traces for process mining, we systematically identify and aggregate attacker behavior that causes security property invalidations. This pipeline enables in-depth understanding of root causes and attack paths leading to protocol-security invalidations. We demonstrate real-world applicability through a prototype and case study on the secure transmission of battery management system data within an automotive network architecture.

cs.CR↗

arXiv2023

Pumping Lemmata for Recognizable Weighted Languages over Artinian Semirings

Pumping lemmata are the main tool to prove that a certain language does not belong to a class of languages like the recognizable languages or the context-free languages. Essentially two pumping lemmata exist for the recognizable weighted languages: the classical one for the Boolean semiring (i.e., the unweighted case), which can be generalized to zero-sum free semirings, and the one for fields. A joint generalization of these two pumping lemmata is provided that applies to all Artinian semirings, over which all finitely generated semimodules have a finite bound on the length of chains of strictly increasing subsemimodules. Since Artinian rings are exactly those that satisfy the Descending Chain Condition, the Artinian semirings include all fields and naturally also all finite semirings (like the Boolean semiring). The new pumping lemma thus covers most previously known pumping lemmata for recognizable weighted languages.

cs.FL↗

arXiv2023

Weighted HOM-Problem for Nonnegative Integers

The HOM-problem asks whether the image of a regular tree language under a given tree homomorphism is again regular. It was recently shown to be decidable by Godoy, Giménez, Ramos, and Àlvarez. In this paper, the N-weighted version of this problem is considered and its decidability is proved. More precisely, it is decidable in polynomial time whether the image of a regular N-weighted tree language under a nondeleting, nonerasing tree homomorphism is regular.

cs.FL↗

arXiv2023

Weighted Tree Automata with Constraints

The HOM problem, which asks whether the image of a regular tree language under a given tree homomorphism is again regular, is known to be decidable [Godoy & Giménez: The HOM problem is decidable. JACM 60(4), 2013]. However, the problem remains open for regular weighted tree languages. It is demonstrated that the main notion used in the unweighted setting, the tree automaton with equality and inequality constraints, can straightforwardly be generalized to the weighted setting and can represent the image of any regular weighted tree language under any nondeleting and nonerasing tree homomorphism. Several closure properties as well as decision problems are also investigated for the weighted tree languages generated by weighted tree automata with constraints.

cs.FL↗

arXiv2022

Strong Equivalence of TAG and CCG

Tree-adjoining grammar (TAG) and combinatory categorial grammar (CCG) are two well-established mildly context-sensitive grammar formalisms that are known to have the same expressive power on strings (i.e., generate the same class of string languages). It is demonstrated that their expressive power on trees also essentially coincides. In fact, CCG without lexicon entries for the empty string and only first-order rules of degree at most 2 are sufficient for its full expressive power.

cs.FL↗

arXiv2018

Recurrent Neural Networks as Weighted Language Recognizers

We investigate the computational complexity of various problems for simple recurrent neural networks (RNNs) as formal models for recognizing weighted languages. We focus on the single-layer, ReLU-activation, rational-weight RNNs with softmax, which are commonly used in natural language processing applications. We show that most problems for such RNNs are undecidable, including consistency, equivalence, minimization, and the determination of the highest-weighted string. However, for consistent RNNs the last problem becomes decidable, although the solution length can surpass all computable bounds. If additionally the string is limited to polynomial length, the problem becomes NP-complete and APX-hard. In summary, this shows that approximations and heuristic algorithms are necessary in practical applications of those RNNs.

cs.FL↗

arXiv2018

Pushing for weighted tree automata

A weight normalization procedure, commonly called pushing, is introduced for weighted tree automata (wta) over commutative semifields. The normalization preserves the recognized weighted tree language even for nondeterministic wta, but it is most useful for bottom-up deterministic wta, where it can be used for minimization and equivalence testing. In both applications a careful selection of the weights to be redistributed followed by normalization allows a reduction of the general problem to the corresponding problem for bottom-up deterministic unweighted tree automata. This approach was already successfully used by Mohri and Eisner for the minimization of deterministic weighted string automata. Moreover, the new equivalence test for two wta $M$ and $M'$ runs in time $\mathcal O((\lvert M \rvert + \lvert M'\rvert) \cdot \log {(\lvert Q\rvert + \lvert Q'\rvert)})$, where $Q$ and $Q'$ are the states of $M$ and $M'$, respectively, which improves the previously best run-time $\mathcal O(\lvert M \rvert \cdot \lvert M'\rvert)$.

cs.FL↗

arXiv2017

Multiple Context-Free Tree Grammars: Lexicalization and Characterization

Multiple (simple) context-free tree grammars are investigated, where "simple" means "linear and nondeleting". Every multiple context-free tree grammar that is finitely ambiguous can be lexicalized; i.e., it can be transformed into an equivalent one (generating the same tree language) in which each rule of the grammar contains a lexical symbol. Due to this transformation, the rank of the nonterminals increases at most by 1, and the multiplicity (or fan-out) of the grammar increases at most by the maximal rank of the lexical symbols; in particular, the multiplicity does not increase when all lexical symbols have rank 0. Multiple context-free tree grammars have the same tree generating power as multi-component tree adjoining grammars (provided the latter can use a root-marker). Moreover, every multi-component tree adjoining grammar that is finitely ambiguous can be lexicalized. Multiple context-free tree grammars have the same string generating power as multiple context-free (string) grammars and polynomial time parsing algorithms. A tree language can be generated by a multiple context-free tree grammar if and only if it is the image of a regular tree language under a deterministic finite-copying macro tree transducer. Multiple context-free tree grammars can be used as a synchronous translation device.

cs.FL↗

arXiv2014

Hyper-Minimization for Deterministic Weighted Tree Automata

Hyper-minimization is a state reduction technique that allows a finite change in the semantics. The theory for hyper-minimization of deterministic weighted tree automata is provided. The presence of weights slightly complicates the situation in comparison to the unweighted case. In addition, the first hyper-minimization algorithm for deterministic weighted tree automata, weighted over commutative semifields, is provided together with some implementation remarks that enable an efficient implementation. In fact, the same run-time O(m log n) as in the unweighted case is obtained, where m is the size of the deterministic weighted tree automaton and n is its number of states.

cs.FL↗

arXiv2013

Random Generation of Nondeterministic Finite-State Tree Automata

Algorithms for (nondeterministic) finite-state tree automata (FTAs) are often tested on random FTAs, in which all internal transitions are equiprobable. The run-time results obtained in this manner are usually overly optimistic as most such generated random FTAs are trivial in the sense that the number of states of an equivalent minimal deterministic FTA is extremely small. It is demonstrated that nontrivial random FTAs are obtained only for a narrow band of transition probabilities. Moreover, an analytic analysis yields a formula to approximate the transition probability that yields the most complex random FTAs, which should be used in experiments.

cs.FL↗

arXiv2013

Composition Closure of Linear Extended Top-down Tree Transducers

Linear extended top-down tree transducers (or synchronous tree-substitution grammars) are popular formal models of tree transformations. The expressive power of compositions of such transducers with and without regular look-ahead is investigated. In particular, the restrictions of nondeletion, epsilon-freeness, and strictness are considered. The composition hierarchy turns out to be finite for all epsilon-free (all rules consume input) variants of these transducers except for nondeleting epsilon-free linear extended top-down tree transducers. The least number of transducers needed for the full expressive power of arbitrary compositions is presented. In all remaining cases (including nondeleting epsilon-free linear extended top-down tree transducers) the composition hierarchy does not collapse.

cs.FL↗

arXiv2011

Optimal Hyper-Minimization

Minimal deterministic finite automata (DFAs) can be reduced further at the expense of a finite number of errors. Recently, such minimization algorithms have been improved to run in time O(n log n), where n is the number of states of the input DFA, by [Gawrychowski and Jeż: Hyper-minimisation made efficient. Proc. MFCS, LNCS 5734, 2009] and [Holzer and Maletti: An n log n algorithm for hyper-minimizing a (minimized) deterministic automaton. Theor. Comput. Sci. 411, 2010]. Both algorithms return a DFA that is as small as possible, while only committing a finite number of errors. These algorithms are further improved to return a DFA that commits the least number of errors at the expense of an increased (quadratic) run-time. This solves an open problem of [Badr, Geffert, and Shipman: Hyper-minimizing minimized deterministic finite state automata. RAIRO Theor. Inf. Appl. 43, 2009]. In addition, an experimental study on random automata is performed and the effects of the existing algorithms and the new algorithm are reported.

cs.FL↗

arXiv2011

On minimising automata with errors

The problem of k-minimisation for a DFA M is the computation of a smallest DFA N (where the size |M| of a DFA M is the size of the domain of the transition function) such that their recognized languages differ only on words of length less than k. The previously best algorithm, which runs in time O(|M| log^2 n) where n is the number of states, is extended to DFAs with partial transition functions. Moreover, a faster O(|M| log n) algorithm for DFAs that recognise finite languages is presented. In comparison to the previous algorithm for total DFAs, the new algorithm is much simpler and allows the calculation of a k-minimal DFA for each k in parallel. Secondly, it is demonstrated that calculating the least number of introduced errors is hard: Given a DFA M and numbers k and m, it is NP-hard to decide whether there exists a k-minimal DFA N differing from DFA M on at most m words. A similar result holds for hyper-minimisation of DFAs in general: Given a DFA M and numbers s and m, it is NP-hard to decide whether there exists a DFA N with at most s states such that DFA M and N differ on at msot m words.

cs.FL↗

arXiv2010

Simulations of Weighted Tree Automata

Simulations of weighted tree automata (wta) are considered. It is shown how such simulations can be decomposed into simpler functional and dual functional simulations also called forward and backward simulations. In addition, it is shown in several cases (fields, commutative rings, Noetherian semirings, semiring of natural numbers) that all equivalent wta M and N can be joined by a finite chain of simulations. More precisely, in all mentioned cases there exists a single wta that simulates both M and N. Those results immediately yield decidability of equivalence provided that the semiring is finitely (and effectively) presented.

cs.FL↗

arXiv2010

Simulation vs. Equivalence

For several semirings S, two weighted finite automata with multiplicities in S are equivalent if and only if they can be connected by a chain of simulations. Such a semiring S is called "proper". It is known that the Boolean semiring, the semiring of natural numbers, the ring of integers, all finite commutative positively ordered semirings and all fields are proper. The semiring S is Noetherian if every subsemimodule of a finitely generated S-semimodule is finitely generated. First, it is shown that all Noetherian semirings and thus all commutative rings and all finite semirings are proper. Second, the tropical semiring is shown not to be proper. So far there has not been any example of a semiring that is not proper.

cs.FL↗

arXiv2009

Properties of quasi-alphabetic tree bimorphisms

We study the class of quasi-alphabetic relations, i.e., tree transformations defined by tree bimorphisms with two quasi-alphabetic tree homomorphisms and a regular tree language. We present a canonical representation of these relations; as an immediate consequence, we get the closure under union. Also, we show that they are not closed under intersection and complement, and do not preserve most common operations on trees (branches, subtrees, v-product, v-quotient, f-top-catenation). Moreover, we prove that the translations defined by quasi-alphabetic tree bimorphism are exactly products of context-free string languages. We conclude by presenting the connections between quasi-alphabetic relations, alphabetic relations and classes of tree transformations defined by several types of top-down tree transducers. Furthermore, we get that quasi-alphabetic relations preserve the recognizable and algebraic tree languages.

cs.CL↗