### Table 1: Complexity of Equivalence

1999

"... In PAGE 10: ... Thus in this case, the rewriting veri#0Ccation problem has exactly the same complexity as checking for equivalence. Therefore, the complexity results obtained in Table1 for equivalence can be easily viewed as complexity results for the rewriting veri#0Ccation problem when we replace q 0 with r u . Verifying disjunctive rewritings has an additional source of complexityover conjunctive rewritings.... ..."

Cited by 75

### Table 1: Complexity of equivalence

"... In PAGE 48: ... A higher data abstraction on dynamic attribute is represented as a nature attribute of moving feature, which is derived from the combination of spatial and temporal information, such as speed, turn, acceleration, range and distance as shown in Table 2. Table1 . Abstract data types of moving feature ST_PointInstant ST_CurveInstant ST_SurfaceInstant ST_SolidInstant ST_PointPeriod ST_CurvePeriod ST_SurfacePeriod ST_SolidPeriod ST_ShapePeriod TM_Instant GM_Point TM_Instant GM_Curve TM_Instant GM_Surface TM_Instant GM_Solid TM_Period GM_Point TM_Period GM_Curve TM_Period GM_Surface TM_Period GM_Solid TM_Period {GM_Primitive} a moving surface whose position is given at given time a moving point whose position is given at given time a moving curve whose position is given at given time a moving curve whose positions change over time a moving solid whose position is given at given time a moving point whose positions change over time a moving shape whose positions change over time as well as size or shape a moving surface whose positions change over time a moving solid whose positions change over time Object type Signature Description Table 2.... In PAGE 86: ... 7 Related Work We briefly state known complexity results for the equivalence problem. Table1 (a) summarizes complexity results for positive relational aggregate queries. Table 1(b) summarizes complexity results for positive aggregate queries (that may have com- parisons).... In PAGE 86: ... Table 1(a) summarizes complexity results for positive relational aggregate queries. Table1 (b) summarizes complexity results for positive aggregate queries (that may have com- parisons). The results from both tables appear in [23, 13, 10].... ..."

### Table 2. Complexity of equivalence and minimality.

1997

"... In PAGE 9: ... In this section we explain which problems have been con- sidered, and give an insight of the results. The results are presented in Table 1 and Table2 . Next section contains some proof sketches.... ..."

Cited by 17

### Table 2. Complexity of equivalence and minimality.

1997

"... In PAGE 9: ... In this section we explain which problems have been con- sidered, and give an insight of the results. The results are presented in Table 1 and Table2 . Next section contains some proof sketches.... ..."

Cited by 17

### Table 6: Complexity of Equivalences with Bounded Relativization in Terms of Completeness Results.

in SEMANTICAL CHARACTERIZATIONS AND COMPUTATIONAL ASPECTS OF EQUIVALENCES IN STABLE LOGIC PROGRAMMING

2005

"... In PAGE 43: ...). Hence, the respective problem classes apply to programs P , Q, only if card(Atm(P [ Q) n A) k. Apparently, this class of problems contains strong and uniform equivalence in its unrelativized versions (k = 0). The complexity results are summarized in Table6 . In particular, we get that in the case of RSE all entries (except Horn/Horn) reduce to coNP-completeness.... ..."

### Table 2: Complex-equivalence relations for mismatching meanings.

### Table 4: Complexity of Uniform Equivalence in Terms of Completeness Results.

in SEMANTICAL CHARACTERIZATIONS AND COMPUTATIONAL ASPECTS OF EQUIVALENCES IN STABLE LOGIC PROGRAMMING

2005

"... In PAGE 32: ... While our main interest is with the problem of deciding uniform equivalence of two given programs, we also consider the related problems of UE-model checking and UE-consequence. Our complexity results for deciding uniform equiv- alence of two given programs are collected from Table 2 into Table4 , for the matter of presentation. The table has to be read as Table 2.... In PAGE 32: ... However, for important classes of programs, it has the same complexity as strong equivalence. In what follows, we prove all the results in Table4 . Towards these results, we start with the problem of UE-model checking.... ..."

### Table 5: Complexity of Relativized Equivalences in Terms of Completeness Results.

in SEMANTICAL CHARACTERIZATIONS AND COMPUTATIONAL ASPECTS OF EQUIVALENCES IN STABLE LOGIC PROGRAMMING

2005

"... In PAGE 37: ... Like in the previous section, we also consider different classes of programs. Our results are summarized in Table5 for both RSE and RUE at a glance by just highlighting where the complexity differs. Note that the only differences between RSE and RUE stem from the entries P 2 =coNP in the column for head-cycle free programs.... In PAGE 38: ...s special cases, i.e., if (V n A) = ;. We deal with bounded relativization explicitly in the subsequent section. Towards deriving the results from Table5 , we first consider model checking problems. Formally, for a set of atoms A, the problem of A-SE-model checking (resp.... ..."

### Table IV. Complexity of Uniform Equivalence in Terms of Completeness Results

2005

Cited by 4

### Table V. Complexity of Relativized Equivalences in Terms of Completeness Results

2005

Cited by 4