Showing papers in "Information & Computation in 1983"
TL;DR: It is proved that there are properties of sequences that are not expressible in temporal logic, even though they are easily expressible using, for instance, regular expressions, and shown how temporal logic can be extended to express any property definable by a right-linear grammar and hence a regular expression.
Abstract: It is first proved that there are properties of sequences that are not expressible in temporal logic, even though they are easily expressible using, for instance, regular expressions. Then, it is shown how temporal logic can be extended to express any property definable by a right-linear grammar and hence a regular expression. Finally, a complete axiomatization and a decision procedure for the extended temporal logic are given and the complexity of the extended logic is examined.
767 citations
TL;DR: Some theorems relating K -density, cut finiteness, and discreteness are proved and the result that a place/transition net is bounded if and only if its processes are K -dense is obtained.
Abstract: The idea of representing non-sequential processes as partially ordered sets (occurrence nets) is applied to place/transition nets (Petri nets), based on the well known notion of process for condition/event-systems. For occurrence nets some theorems relating K -density, cut finiteness, and discreteness are proved. With these theorems the result that a place/transition net is bounded if and only if its processes are K -dense is obtained.
320 citations
TL;DR: It is shown that Th( L ), the set of sentences (of type L ) true almost everywhere, is complete in PSPACE and various upper and lower bounds of the complexity of this theory are obtained.
Abstract: A first-order sentence of a relational type L is true almost everywhere if the proportion of its models among the structures of type L and cardinality m tends to 1 when m tends to ∞. It is shown that Th( L ) , the set of sentences (of type L ) true almost everywhere, is complete in PSPACE. Further, various upper and lower bounds of the complexity of this theory are obtained. For example, if the arity of the relation symbols of L is d ⩾ 2 and if Pr Th( L ) is the set of prenex sentences of Th( L ) , then Pr Th( L ) ∈ DSPACE(( n / log n ) d ) and Pr Th( L ) ∉ NTIME ( o ( n / log n ) d ) . If R is a binary relation symbol and L = { R } , ( Th ( L ) is the theory of almost all graphs), then Pr Th ( L ) ∉ NSPACE ( o ( n / log n ) ) . These results are optimal modulo open problems in complexity such as NTIME(T)? DSPACE(T) and NSPACE(S) = ? DSPACE(S2).
55 citations
TL;DR: The algorithm uses several new ideas including: (1) It removes portions of the graph and replaces them with groups which are used to keep track of the symmetries of these portions, and (2) It maintains with each group a tower of equivalence relations which allow a decomposition of the group.
Abstract: A polynomial time isomorphism test for graphs called k-contractible graphs for fixed k is included. The class of k-contractible graphs includes the graphs of bounded valence and the graphs of bounded genus. The algorithm uses several new ideas including: (1) It removes portions of the graph and replaces them with groups which are used to keep track of the symmetries of these portions. (2) It maintains with each group a tower of equivalence relations which allow a decomposition of the group. These towers are called towers of Γk-actions.
45 citations
TL;DR: A polynomial time algorithm for testing isomorphism of graphs which are pairwise k-separable for fixed k is given, which is a natural generalization of the bounded valence test of Luks.
Abstract: A polynomial time algorithm for testing isomorphism of graphs which are pairwise k-separable for fixed k is given. The pairwise k-separable graphs are those graphs where each pair of distinct vertices are k-separable. This is a natural generalization of the bounded valence test of Luks. The subgroup of automorphisms of a hypergraph whose restriction to the vertices is in a given Γk group, for fixed k is constructed in polynomial time.
38 citations
TL;DR: N nondeterminism adds to the expressive power even in the presence of quantifiers, and the proof here, unlike that of Berman, Halpern, and Tiuryn (1982, in “Automata, Language, and Programming,” Springer, Berlin), holds in the absence of first-order tests as well as quantifier-free tests.
Abstract: There is a language L and structures A1 and A2 for L such that, for each closed formula F of deterministic regular dynamic logic, the formula F is valid in A1 if and only if F is valid in A2. There is, however, a closed formula of nondeterministic regular dynamic logic is both valid in A1 and not valid in A2. Thus, nondeterminism adds to the expressive power even in the presence of quantifiers. This answers Meyer's question. Moreover, the proof here, unlike that of Berman, Halpern, and Tiuryn (1982, in “Automata, Language, and Programming,” Springer, Berlin), holds in the presence of first-order tests as well as quantifier-free tests.
25 citations
TL;DR: If the machine is allowed a random access input, then the time bound can be improved so that the time-space product is O(n1 + ɛ).
Abstract: Let S(n) be a nice space bound such that log2 n ⩽ S(n) ⩽ n. Then every DCFL is recognized by a multitape Turing machine simultaneously in time O(n2/S(n)) and space O(S(n)), and this time bound is optimal. If the machine is allowed a random access input, then the time bound can be improved so that the time-space product is O(n1 + ɛ).
23 citations
TL;DR: It is proved that a recursive program is able to enumerate all elements in any Herbrand interpretation if there are first-order formulas expressing integer arithmetic in that interpretation.
Abstract: It is proved that a recursive program (without counters) is able to enumerate all elements in any Herbrand interpretation. It follows that all recursive program domains in a Herbrand interpretation can be defined by first-order formulas iff there are first-order formulas expressing integer arithmetic in that interpretation.
18 citations
TL;DR: As a conclusion it is obtained that for error-control purposes none of the investigated superclasses of the class of convolutional codes is better suited than theclass of convolutionsal codes itself.
Abstract: The present paper is a self-contained treatment of subspaces of the space GF( q ) ω of all semi-infinite strings over GF( q ). Some necessary and sufficient conditions which characterize those subspaces of GF( q ) ω are derived which are convolutional codes, and the classes of subspaces defined by one or more of them are investigated. Moreover structural parameters of convolutional codes such as block length, rate, delay, and constraint length are considered as parameters of subspaces rather than parameters of an encoding device. As a conclusion it is obtained that for error-control purposes none of the investigated superclasses of the class of convolutional codes is better suited than the class of convolutional codes itself.
13 citations
TL;DR: The complete axiomatization of termination assertions is an axiomatic definition of the semantics of recursive programs.
Abstract: The termination assertion p〈S〉 q means that whenever the formula p is true, there is an execution of the possibly nondeterministic program S which terminates in a state in which q is true. The program S may declare and use local variables and nondeterministic procedures with call-by-value and call-by-address parameters. In addition, the program may call undeclared global procedures. Formulas p and q are first-order formulas extended to express hypotheses about the termination of calls to undeclared procedures. A complete effective axiom system with rules corresponding to the syntax of the programming language is given for the termination assertions valid over all interpretations. Termination assertions define the semantics of programs in the following sense: if two programs have different input-output semantics, then there is a temination assertion that is valid for one program but not the other. Thus the complete axiomatization of termination assertions is an axiomatic definition of the semantics of recursive programs.
10 citations
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