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Tree Automata for Code Selection
, 1994
"... We deal with the generation of code selectors in compiler backends. The fundamental concepts are systematically derived from the theory of regular tree grammars and finite tree automata. We use this general approach to construct algorithms that generalize and improve existing methods. 1 Introduction ..."
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We deal with the generation of code selectors in compiler backends. The fundamental concepts are systematically derived from the theory of regular tree grammars and finite tree automata. We use this general approach to construct algorithms that generalize and improve existing methods. 1 Introduction A code generator for a compiler is applied to an intermediate representation (IR) of the input program that has been computed during preceding phases of compilation. This intermediate representation can be viewed as code for an abstract machine. The task of code generation is to translate this code into an efficient sequence of instructions for a concrete machine. Besides register allocation and instruction scheduling (for processors with pipelined architectures), code selection, i.e., the selection of instructions, is one subtask of code generation. It is especially important for CISC (Complex I nstruction Set Computer) architectures where there are usually many possibilities to generat...
Treeshifts of finite type
, 2011
"... A onesided (resp. twosided) shift of finite type of dimension one can be described as the set of infinite (resp. biinfinite) sequences of consecutive edges in a finitestate automaton. While the conjugacy of shifts of finite type is decidable for onesided shifts of finite type of dimension one, ..."
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Cited by 1 (1 self)
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A onesided (resp. twosided) shift of finite type of dimension one can be described as the set of infinite (resp. biinfinite) sequences of consecutive edges in a finitestate automaton. While the conjugacy of shifts of finite type is decidable for onesided shifts of finite type of dimension one, the result is unknown in the twosided case. In this paper, we study the shifts of finite type defined by infinite ranked trees. Indeed, infinite ranked trees have a natural structure of symbolic dynamical systems. We prove a Decomposition Theorem for these treeshifts, i.e. we show that a conjugacy between two treeshifts can be broken down into a finite sequence of elementary transformations called insplittings and inamalgamations. We prove that the conjugacy problem is decidable for treeshifts of finite type. This result makes the class of treeshifts closer to the class of onesided shifts of sequences than to the class of twosided ones. Our proof uses the notion of bottomup tree automata. 1