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Tree Automata as Algebras: Minimisation and Determinisation [article]

Gerco van Heerdt, Tobias Kappé, Jurriaan Rot, Matteo Sammartino, Alexandra Silva
2019 arXiv   pre-print
We study a categorical generalisation of tree automata, as Σ-algebras for a fixed endofunctor Σ endowed with initial and final states.  ...  Under mild assumptions about the base category, we present a general minimisation algorithm for these automata.  ...  The functor V can be viewed as a determinisation construction for (Σ, S)-tree automata.  ... 
arXiv:1904.08802v1 fatcat:viekhxtihfcn3jrujycshvroii

On Probabilistic Kleene Algebras, Automata and Simulations [chapter]

Annabelle McIver, Tahiry M. Rabehaja, Georg Struth
2011 Lecture Notes in Computer Science  
Hence an identity is valid in continuous probabilistic Kleene algebras if and only if the associated automata are simulation equivalent.  ...  We show that a class of automata modulo simulation equivalence forms a model of probabilistic Kleene algebra.  ...  We would like to thank Ernie Cohen and Hitoshi Furusawa for helpful discussions, and to Jeff Sanders for valuable comments.  ... 
doi:10.1007/978-3-642-21070-9_20 fatcat:2x62n4brdbbefku4afxkvd4tvq

An Efficient Coq Tactic for Deciding Kleene Algebras [chapter]

Thomas Braibant, Damien Pous
2010 Lecture Notes in Computer Science  
We present a reflexive tactic for deciding the equational theory of Kleene algebras in the Coq proof assistant.  ...  This tactic relies on a careful implementation of efficient finite automata algorithms, so that it solves casual equations almost instantaneously.  ...  non-deterministic finite automata (NFA); 3. determinise the automata to obtain deterministic finite automata (DFA); 4. check that the two DFAs are equivalent.  ... 
doi:10.1007/978-3-642-14052-5_13 fatcat:5dcm5rz4jrcohh55ectexyd7gu

Minimisation in Logical Form [article]

Nick Bezhanishvili and Marcello Bonsangue and Helle Hvid Hansen and Dexter Kozen and Clemens Kupke and Prakash Panangaden and Alexandra Silva
2020 arXiv   pre-print
Examples include partially observable deterministic finite automata, linear weighted automata viewed as coalgebras over finite-dimensional vector spaces, and belief automata, which are coalgebras on compact  ...  In Bezhanishvili et al. (2012), a dual equivalence between a category of coalgebras and a category of algebras was used to explain minimisation.  ...  We will use the determinisation construction in order to place alternating automata and weighted automata in our general minimisation framework.  ... 
arXiv:2005.11551v1 fatcat:v72fxl3yj5dd5gr3qteo6rxvaa

A String Diagrammatic Axiomatisation of Finite-State Automata [article]

Robin Piedeleu, Fabio Zanasi
2020 arXiv   pre-print
First, the Kleene star is a derived concept, as it can be decomposed into more primitive algebraic blocks.  ...  We develop a fully diagrammatic approach to the theory of finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams  ...  Minimisation and completeness As explained above, our proof of completeness is a diagrammatic reformulation of Brzozowski's algorithm which proceeds in four steps: determinise, reverse, determinise, reverse  ... 
arXiv:2009.14576v2 fatcat:74tkq5te2nbffdh6nfeg3bcjyq

Penrose: Putting Compositionality to Work for Petri Net Reachability [chapter]

Paweł Sobociński, Owen Stephens
2013 Lecture Notes in Computer Science  
We introduce a tool that uses this technique, Penrose, discuss some design details in its implementation, and identify potential future improvements.  ...  investigate applying our decomposition technique to model checking problems other than reachability; optimising BDD representation, particularly w.r.t. the performance of the NFA to minimal DFA procedure; and  ...  Indeed, Penrose performs well only if small automata are minimised.  ... 
doi:10.1007/978-3-642-40206-7_29 fatcat:rbhhbfcszzdx7c3p5kqze3eggq

An Efficient Finite Tree Automata Library [article]

Ondřej Lengál
2012 arXiv   pre-print
The present paper first describes the theoretical background of finite tree automata and regular tree languages.  ...  These data structures have often the character of trees or they can be encoded as trees with some additional pointers.  ...  The minimisation process starts with pruning unreachable states and determinising the input automaton.  ... 
arXiv:1204.3240v1 fatcat:mzkxqmjemjeplnoy2kmizjwzvi

Coalgebraic Tools for Bisimilarity and Decorated Trace Semantics [article]

Georgiana Caltais
2015 arXiv   pre-print
The aim of this thesis is to exploit the strengths of the (co)algebraic framework in modelling reactive systems and reasoning on several types of associated semantics, in a uniform fashion.  ...  semantics for labelled transition systems and probabilistic systems, and testing semantics for labelled transition systems with internal behaviour.  ...  I truly appreciate their flexibility, understanding and willingness  ... 
arXiv:1502.02910v1 fatcat:dypxhnudsnfqznjeg244p2u54a

Lazy Probabilistic Model Checking without Determinisation

Ernst Moritz Hahn, Guangyuan Li, Sven Schewe, Andrea Turrini, Lijun Zhang, Marc Herbstritt
2015 International Conference on Concurrency Theory  
The bottleneck in the quantitative analysis of Markov chains and Markov decision processes against specifications given in LTL or as some form of nondeterministic Büchi automata is the inclusion of a determinisation  ...  In this paper, we show that full determinisation can be avoided: subset and breakpoint constructions suffice. We have implemented our approach-both explicit and symbolic versions-in a prototype tool.  ...  minimising instead of maximising.  ... 
doi:10.4230/lipics.concur.2015.354 dblp:conf/concur/HahnLST015 fatcat:ffztb2b7kjhc5o7xlcs5ps242m

Higher Dimensional Trees, Algebraically [chapter]

Neil Ghani, Alexander Kurz
Algebra and Coalgebra in Computer Science  
This paper presents an alternative approach which focusses more on their universal properties and is based upon category theory, algebras, coalgebras and containers.  ...  the core theory of the formal languages of strings and trees to these higher dimensions.  ...  Determinisation and Minimisation This section follows the work by Arbib and Manes [2] [3] [4] on automata as algebras for a functor on a category.  ... 
doi:10.1007/978-3-540-73859-6_16 dblp:conf/calco/GhaniK07 fatcat:zrvya35gpvdmba7yeevjz6g44y

Simulations and Antichains for Efficient Handling of Finite Automata [article]

Lukáš Holík
2017 arXiv   pre-print
We give efficient algorithms for computing tree automata simulations and we also introduce a new type of relation that arises from a combination of tree automata downward and upward simulation and that  ...  tree automata.  ...  A classical approach to cope with these problems is determinisation. Both FA as well as TA can be determinised and minimised in a canonical way.  ... 
arXiv:1706.03208v1 fatcat:qmzaknz5xnfy5lmjp426jjlf5a

Containment and Equivalence of Weighted Automata: Probabilistic and Max-Plus Cases [chapter]

Laure Daviaud
2020 Lecture Notes in Computer Science  
This paper surveys some results regarding decision problems for probabilistic and max-plus automata, such as containment and equivalence.  ...  Probabilistic and max-plus automata are part of the general family of weighted automata, whose semantics are maps from words to real values.  ...  as trees [4, 29, 38] .  ... 
doi:10.1007/978-3-030-40608-0_2 fatcat:gexpjfbjszfujmedra5va2ojsa

Checking NFA equivalence with bisimulations up to congruence

Filippo Bonchi, Damien Pous
2013 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '13  
We introduce bisimulation up to congruence as a technique for proving language equivalence of non-deterministic finite automata.  ...  from the fact that {x} is related to {u} and {y} to {v, w}, without the need of further exploring the determinised automaton.  ...  As future work, we plan to extend our approach to tree automata. In particular, it seems promising to investigate if further up-to techniques can be defined for regular tree expressions.  ... 
doi:10.1145/2429069.2429124 dblp:conf/popl/BonchiP13 fatcat:72ghke65afhgpgyp2tb2jglfye

Checking NFA equivalence with bisimulations up to congruence

Filippo Bonchi, Damien Pous
2013 SIGPLAN notices  
We introduce bisimulation up to congruence as a technique for proving language equivalence of non-deterministic finite automata.  ...  from the fact that {x} is related to {u} and {y} to {v, w}, without the need of further exploring the determinised automaton.  ...  As future work, we plan to extend our approach to tree automata. In particular, it seems promising to investigate if further up-to techniques can be defined for regular tree expressions.  ... 
doi:10.1145/2480359.2429124 fatcat:mb4pqiyibrgtro4sify3ywb27e

Polymorphism, subtyping, and type inference in MLsub

Stephen Dolan, Alan Mycroft
2017 Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages - POPL 2017  
Principal types are kept compact by type simplification, which exploits deep connections between subtyping and the algebra of regular languages. An implementation is available online.  ...  constraints between these input and output types.  ...  This work was funded by Trinity College, Cambridge, and OCaml Labs.  ... 
doi:10.1145/3009837.3009882 fatcat:ps4tknkfkvfqrnyrfadohw5lcm
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