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Equational axioms for probabilistic bisimilarity
 IN PROCEEDINGS OF 9TH AMAST, LECTURE NOTES IN COMPUTER SCIENCE
, 2002
"... This paper gives an equational axiomatization of probabilistic bisimulation equivalence for a class of finitestate agents previously studied by Stark and Smolka ((2000) Proof, Language, and Interaction: Essays in Honour of Robin Milner, pp. 571595). The axiomatization is obtained by extending ..."
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This paper gives an equational axiomatization of probabilistic bisimulation equivalence for a class of finitestate agents previously studied by Stark and Smolka ((2000) Proof, Language, and Interaction: Essays in Honour of Robin Milner, pp. 571595). The axiomatization is obtained by extending the general axioms of iteration theories (or iteration algebras), which characterize the equational properties of the fixed point operator on (#)continuous or monotonic functions, with three axiom schemas that express laws that are specific to probabilistic bisimilarity.
Solving and factoring boundary problems for linear ordinary differential equations in differential algebras
 Journal of Symbolic Computation
"... We present a new approach for expressing and solving boundary problems for linear ordinary differential equations in the language of differential algebras. Starting from an algebra with a derivation and integration operator, we construct a ring of linear integrodifferential operators that is expres ..."
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Cited by 16 (12 self)
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We present a new approach for expressing and solving boundary problems for linear ordinary differential equations in the language of differential algebras. Starting from an algebra with a derivation and integration operator, we construct a ring of linear integrodifferential operators that is expressive enough for specifying regular boundary problems with arbitrary Stieltjes boundary conditions as well as their solution operators. Based on these structures, we define a new multiplication on regular boundary problems in such a way that the resulting Green’s operator is the reverse composition of the constituent Green’s operators. We provide also a method for lifting any factorization of the underlying differential operator to the level of boundary problems. Since this method only needs the computation of initial value problems, it can be used as an effective alternative for computing Green’s operators in case one knows how to factor the given differential operators.
Random Group Automata
, 2000
"... A group automaton is a complete deterministic automaton such that each letter of the alphabet acts on the set of states as a permutation [1, 5]. The aim is to describe an algorithm for the random generation of a minimal group automaton with n states. The treatment is largely based on properties of r ..."
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A group automaton is a complete deterministic automaton such that each letter of the alphabet acts on the set of states as a permutation [1, 5]. The aim is to describe an algorithm for the random generation of a minimal group automaton with n states. The treatment is largely based on properties of random permutations and random automata. 1. Properties A group automaton is a complete deterministic automaton such that each letter of the alphabet acts on the set of states as a permutation [1, 5]. We consider a group automaton A, with states 1, 2, : : : , n. The state 1 is the initial state; the set of final states is denoted by F , the alphabet by a, b, : : : , and the transitions by q 2 = ffi(q 1 ; a) or equivalently (q 1 ; a; q 2 ). 1 2 3 4 start a a b a b b a,b Figure 1. a group automaton Let us recall that two states q 1 and q 2 of an automaton are equivalent, notationally q 1 q 2 , if for every word u, the state ffi(q 1 ; u) belongs to F if and only if ffi(q 2 ; u) belongs to F . ...
cernyJournalFinal A QUADRATIC UPPER BOUND ON THE SIZE OF A SYNCHRONIZING WORD IN ONECLUSTER AUTOMATA
"... Čern´y’s conjecture asserts the existence of a synchronizing word of length at most (n− 1) 2 for any synchronized nstate deterministic automaton. We prove a quadratic upper bound on the length of a synchronizing word for any synchronized nstate deterministic automaton satisfying the following addi ..."
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Čern´y’s conjecture asserts the existence of a synchronizing word of length at most (n− 1) 2 for any synchronized nstate deterministic automaton. We prove a quadratic upper bound on the length of a synchronizing word for any synchronized nstate deterministic automaton satisfying the following additional property: there is a letter a such that for any pair of states p,q, one has p·a r = q·a s for some integers r,s (for a state p and a word w, we denote by p·w the state reached from p by the path labeled w). As a consequence, we show that for any finite synchronized prefix code with an nstate decoder, there is a synchronizing word of length O(n 2). This applies in particular to Huffman codes.
www.elsevier.com/locate/tcs Another proof of Soittola’s theorem
"... Soittola’s theorem characterizes R+ or Nrational formal power series in one variable among the rational formal power series with nonnegative coefficients. We present here a new proof of the theorem based on Soittola’s and Perrin’s proofs together with some new ideas that allows us to separate alge ..."
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Soittola’s theorem characterizes R+ or Nrational formal power series in one variable among the rational formal power series with nonnegative coefficients. We present here a new proof of the theorem based on Soittola’s and Perrin’s proofs together with some new ideas that allows us to separate algebraic and analytic arguments. c ○ 2008 Elsevier B.V. All rights reserved.