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Proving Properties of Incremental Merkle Trees [chapter]

Mizuhito Ogawa, Eiichi Horita, Satoshi Ono
2005 Lecture Notes in Computer Science  
This paper proves two basic properties of the incremental construction of a Merkle tree: (1) correctness of completion and (2) correctness of an incremental sanity check.  ...  Sections 2 and 3 explain what Merkle trees and MONA are, respectively.  ...  Proving consistency For the latter half of the proof of Theorem 2, we will prove that if {(LSR ti+1 (t i ), α i ) | 1 ≤ i < k} ∪ {(LS(t k ), α k )} is weakly consistent, they are consistent.  ... 
doi:10.1007/11532231_31 fatcat:c4jl6hs3lnbwdixtls7bc4lhia

Proving Data-Poisoning Robustness in Decision Trees [article]

Samuel Drews and Aws Albarghouthi and Loris D'Antoni
2020 arXiv   pre-print
Antidote abstractly trains decision trees for an intractably large space of possible poisoned datasets.  ...  We study the problem of proving that a prediction is robust to data poisoning, where an attacker can inject a number of malicious elements into the training set to influence the learned model.  ...  Table 1 shows that test set 9 accuracies of the decision trees learned by DTrace are reasonably highaffirmation that when we prove the robustness of its results, we are proving something worthwhile.  ... 
arXiv:1912.00981v2 fatcat:tk6ep2amnjhgljbr3ngmewdwpy

Proving tree algorithms for succinct data structures [article]

Reynald Affeldt, Jacques Garrigue, Xuanrui Qi, Kazunari Tanaka
2019 arXiv   pre-print
We present here the formalization in Coq/SSReflect of two different tree-based succinct representations and their accompanying algorithms.  ...  One is the Level-Order Unary Degree Sequence, which encodes the structure of a tree in breadth-first order as a sequence of bits, where access operations can be defined in terms of Rank and Select, which  ...  However, we need to use wf_dtree when we prove properties of dinsert, as it modifies the tree. Definition Proving (a) and (b) involves no theoretical difficulty.  ... 
arXiv:1904.02809v2 fatcat:aqzki67cwzf2tdpkfw62uxf3im

Tree-Residue Vertex-Breaking: a new tool for proving hardness [article]

Erik D. Demaine, Mikhail Rudoy
2018 arXiv   pre-print
In this paper, we introduce a new problem called Tree-Residue Vertex-Breaking (TRVB): given a multigraph G some of whose vertices are marked "breakable," is it possible to convert G into a tree via a sequence  ...  We also demonstrate a connection between TRVB and the Hypergraph Spanning Tree problem.  ...  We would also like to thank Yahya Badran for pointing out the connection between TRVB and the Hypergraph Spanning Tree problem.  ... 
arXiv:1706.07900v3 fatcat:ngjh5zwdrffappelaghyjmidnq

Quickly proving Diestel's normal spanning tree criterion [article]

Max Pitz
2020 arXiv   pre-print
We present two short proofs for Diestel's criterion that a connected graph has a normal spanning tree provided it contains no subdivision of a countable clique in which every edge has been replaced by  ...  Tree orders and normal trees We follow the notation in [1] . The tree-order T of a tree T with root r is defined by setting u T v if u lies on the unique path from r to v in T .  ...  A rooted spanning tree T of a graph G is called normal if the end vertices of any edge of G are comparable in the natural tree order of T .  ... 
arXiv:2006.02994v1 fatcat:4igk7mguazhk7pwyrk5jrqrsdu

Quickly Proving Diestel's Normal Spanning Tree Criterion

Max Pitz
2021 Electronic Journal of Combinatorics  
We present two short proofs for Diestel's criterion that a connected graph has a normal spanning tree provided it contains no subdivision of a countable clique in which every edge has been replaced by  ...  Tree orders and normal trees We follow the notation in [1] . The tree-order T of a tree T with root r is defined by setting u T v if u lies on the unique path from r to v in T .  ...  Let G be a graph with a normal spanning tree. Then for every connected subgraph C ⊆ G and every r ∈ C there is a normal spanning tree of C with root r.  ... 
doi:10.37236/9619 fatcat:3lpswqaqjjf65cggpnkyf4ed2i

Proving lower bounds for linear decision trees [chapter]

Marc Snir
1981 Lecture Notes in Computer Science  
It is therefore interesting to develop new methods for proving lower bounds on the complexity of linear decision trees.  ...  THE INFOrmaTION THEORETIC ARGUMENT AND ITS EXTENSIONS The m o s t general argument used to prove lower bounds on decision trees is the inform&tion theoretic one: if the problem P is defined by m sets then  ... 
doi:10.1007/3-540-10843-2_25 fatcat:ld6pocfjanci5ohz45bapz5cje

Proving Tree Algorithms for Succinct Data Structures

Reynald Affeldt, Jacques Garrigue, Xuanrui Qi, Kazunari Tanaka, Michael Wagner
2019 International Conference on Interactive Theorem Proving  
We present here the formalization in Coq/SSReflect of two different tree-based succinct representations and their accompanying algorithms.  ...  One is the Level-Order Unary Degree Sequence, which encodes the structure of a tree in breadth-first order as a sequence of bits, where access operations can be defined in terms of Rank and Select, which  ...  However, we need to use wf_dtree when we prove properties of dinsert, as it modifies the tree. Proving (a) and (b) involves no theoretical difficulty.  ... 
doi:10.4230/lipics.itp.2019.5 dblp:conf/itp/AffeldtGQT19 fatcat:wjm26dgrsjhffg47qk3sh4uixu

Inductive theorem proving based on tree grammars

Sebastian Eberhard, Stefan Hetzl
2015 Annals of Pure and Applied Logic  
S(F ) is a tautology 5. π := proof induced by S(F ) Output: inductive proof π of Γ ⊢ ∀x A(x) a tautology Outline Cut-elimination and cut-introduction ⇒ Inductive theorem proving based on tree grammars  ...  . , t n } -a (finite) tree language. ◮ Theorem (H 2012). If π is a proof with Π 1 -cuts then there is a totally rigid acyclic tree grammar G (π) s.t.  ... 
doi:10.1016/j.apal.2015.01.002 fatcat:xje7pm5nlfdjfnd3dqzy3rcrvy

Proving identities on weight polynomials of tiered trees via Tutte polynomials [article]

Fengming Dong, Sherry H.F. Yan
2021 arXiv   pre-print
In this article, we will prove an extension of this identity by applying Tutte polynomials.  ...  For any ordered partition p=(p_1,p_2,⋯,p_m) of n, let _p denote the set of tiered trees with vertex set n and with a map t: n→m such that |t^-1(i)|=p_i for all i=1,2,...,m.  ...  We prove this result by showing the following claims. This completes the proof of Claim 2.  ... 
arXiv:2003.00625v2 fatcat:2fwcvfkns5genkpmuug27nfzoy

Towards Formal Fault Tree Analysis using Theorem Proving [article]

Waqar Ahmed, Osman Hasan
2015 arXiv   pre-print
Fault Tree Analysis (FTA) is a dependability analysis technique that has been widely used to predict reliability, availability and safety of many complex engineering systems.  ...  In particular, the paper presents a higher-order-logic formalization of generic Fault Tree gates, i.e., AND, OR, NAND, NOR, XOR and NOT and the formal verification of their failure probability expressions  ...  GatesFault Tree Gates HOL Formalization Table 2 : 2 Probability of Failure of Fault Tree Gates Fault Tree Gates Theorem's Conclusion Solar FT p x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 t  ... 
arXiv:1505.02648v1 fatcat:7ulnrqywubcr3merkju53dfppe

Proving that a Tree Language is not First-Order Definable [article]

Martin Beaudry
2018 arXiv   pre-print
We explore from an algebraic viewpoint the properties of the tree languages definable with a first-order formula involving the ancestor predicate, using the description of these languages as those recognized  ...  This research started with the intention of understanding the mechanisms that underlie the Ehrenfeucht-Fraïssé games used to prove that a forest algebra lies outside of * * N τ,π .  ...  Finally, a forest with at least one tree in L tree g and no tree in L tree k for any k ∈ G out will belong to L g iff everyone of its other trees belongs to h∈G X L tree h .  ... 
arXiv:1812.01674v1 fatcat:beb5kttocjdenkeebx2ljcsuje

A Decision Tree Abstract Domain for Proving Conditional Termination [chapter]

Caterina Urban, Antoine Miné
2014 Lecture Notes in Computer Science  
The elements of the abstract domain are decision trees where the decision nodes are labeled with linear constraints, and the leaf nodes belong to a numerical abstract domain.  ...  We have implemented a static analyzer for proving conditional termination of programs written in (a subset of) C and, using experimental evidence, we show that it performs well on a wide variety of benchmarks  ...  able to prove termination for.  ... 
doi:10.1007/978-3-319-10936-7_19 fatcat:thg3xy4jjbag5mxea7b256p4yi

Dynamic Fault Trees Analysis using an Integration of Theorem Proving and Model Checking [article]

Yassmeen Elderhalli, Osman Hasan, Waqar Ahmad, Sofiene Tahar
2017 arXiv   pre-print
Dynamic fault trees (DFTs) have emerged as an important tool for capturing the dynamic behavior of system failure.  ...  To overcome these limitations, we propose a comprehensive methodology to perform the qualitative and quantitative analysis of DFTs using an integration of theorem proving and model checking based approaches  ...  FTs can be categorized as Static Fault trees (SFT) and Dynamic Fault trees (DFT) [1] .  ... 
arXiv:1712.02872v1 fatcat:xxpxgog3cnevfazych5hs5iliy

PROVING THE CORRECTNESS CONDITIONS OF THE THREE-WAY HANDSHAKE PROTOCOL USING COMPUTATIONAL TREE LOGIC

RAFAT ALSHORMAN AHMAD ALOMARI
2021 Zenodo  
In this research, we used the NuSMV model checker along with Computational Tree Logic (CTL) to verify the correctness of the three-way handshake protocol over specific correctness conditions and properties  ...  The temporal logic is divided into two models; the Computation Tree Logic (CTL), and the Linear Time Logic (LTL).  ...  The CTL is a type of logic where the time is branched in a form of a tree structure and called branching time logic [3] .  ... 
doi:10.5281/zenodo.5353200 fatcat:5zzaekqzrndoxgkzgnrgh3h4tm
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